Is it Hard for Biological Neural Networks To Learn the Game of Life, too?

examples.txt

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┃    ▓    ▓  ▓▓  ▓▓▓▓▓   ▓▓▓     ┃    ┃           ▓▓▓  ▓▓▓▓▓    ▓▓     ┃
┃▓ ▓ ▓▓  ▓▓▓ ▓   ▓▓ ▓▓ ▓  ▓  ▓  ▓┃    ┃                ▓▓▓▓▓           ┃
┃ ▓ ▓  ▓       ▓ ▓▓▓ ▓▓  ▓ ▓ ▓▓ ▓┃    ┃                ▓▓▓▓▓           ┃
┃  ▓ ▓ ▓     ▓  ▓        ▓  ▓ ▓ ▓┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓▓    ▓ ▓▓▓ ▓ ▓ ▓▓  ▓▓▓     ┃    ┃           ▓▓▓▓▓▓▓▓▓▓    ▓▓     ┃
┃  ▓ ▓ ▓▓▓▓▓▓▓▓▓▓ ▓▓▓▓ ▓▓ ▓▓  ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓▓ ▓▓▓ ▓    ▓▓▓  ▓▓ ▓  ▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓┃
┃  ▓▓▓ ▓  ▓▓▓ ▓    ▓▓ ▓ ▓ ▓▓▓▓ ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓  ▓▓┃
┃▓ ▓ ▓ ▓ ▓▓   ▓ ▓▓ ▓▓  ▓ ▓  ▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓       ▓  ▓▓┃
┃  ▓▓▓▓ ▓  ▓ ▓▓▓  ▓         ▓▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓   ░        ▓    ┃
┃ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓   ▓ ▓ ▓▓ ▓ ▓ ▓ ▓┃    ┃  ▓▓▓▓░▓▓▓▓▓▓▓▓       ▓▓  ▓▓    ┃
┃▓        ▓▓▓    ▓▓▓  ▓▓▓ ▓▓▓▓   ┃    ┃         ▓▓▓▓     ▓▓  ▓▓  ▓▓    ┃
┃▓ ▓▓ ▓▓   ▓ ▓▓     ▓▓    ▓      ┃    ┃         ▓▓▓▓     ▓▓            ┃
┃ ▓   ▓ ▓▓▓▓▓▓ ▓   ▓▓ ▓   ▓ ▓▓▓▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓    ▓▓        ▓▓▓▓┃
┃ ▓  ▓▓▓▓▓ ▓▓▓▓▓ ▓ ▓    ▓    ▓▓▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓              ▓▓▓▓┃
┃▓▓▓▓    ▓  ▓   ▓▓   ▓▓▓   ▓▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓              ▓▓▓▓▓┃
┃▓ ▓ ▓▓ ▓▓ ▓▓▓▓   ▓▓▓     ▓▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓            ▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓▓ ▓▓▓▓     ▓  ▓    ▓▓▓   ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓     ▓▓▓▓   ┃
┃▓ ▓ ▓▓  ▓▓  ▓   ▓▓ ▓▓▓▓▓▓ ▓▓▓▓  ┃    ┃  ▓▓▓▓  ▓▓▓     ▓▓▓▓▓▓▓▓ ▓▓▓▓   ┃
┃  ▓▓   ▓  ▓     ▓▓▓  ▓▓    ▓▓ ▓▓┃    ┃         ▓▓     ▓▓▓▓▓▓▓▓  ▓▓▓   ┃
┃▓        ▓▓ ▓▓ ▓▓▓▓▓▓ ▓▓ ▓▓    ▓┃    ┃         ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃  ▓▓  ▓▓ ▓▓ ▓▓ ▓▓ ▓▓▓ ▓▓   ▓ ▓▓ ┃    ┃  ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓┃
┃  ▓▓▓  ▓   ▓ ▓▓▓ ▓  ▓ ▓▓ ▓▓  ▓▓▓┃    ┃  ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓┃
┃▓▓  ▓ ▓▓▓▓   ▓ ▓▓  ▓ ▓▓  ▓  ▓ ▓▓┃    ┃▓▓  ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓┃
┃▓▓  ▓▓▓ ▓▓ ▓ ▓▓  ▓  ▓▓ ▓    ▓▓  ┃    ┃▓▓  ▓▓▓▓▓▓  ▓▓▓▓▓░▓▓▓▓▓         ┃
┃  ▓▓  ▓ ▓▓  ▓▓  ▓ ▓▓▓  ▓ ▓ ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓  ▓▓▓▓░▓▓▓▓▓          ┃
┃ ▓▓▓ ▓▓ ▓  ▓▓ ▓  ▓   ▓  ▓▓▓   ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓  ▓▓▓     ┃
┃▓▓▓  ▓▓ ▓ ▓   ▓ ▓ ▓▓▓   ▓▓   ▓ ▓┃    ┃▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓   ▓▓▓     ┃
┃▓▓▓  ▓▓ ▓▓▓ ▓▓▓▓▓ ▓▓ ▓▓▓ ▓▓▓   ▓┃    ┃▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓┃
┃▓▓ ▓▓  ▓ ▓▓▓▓  ▓▓  ▓  ▓   ▓  ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░         ▓▓▓┃
┃  ▓▓▓ ▓ ▓ ▓  ▓▓▓  ▓  ▓▓ ▓ ▓  ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ▓▓ ┃
┃ ▓▓▓▓▓▓▓  ▓ ▓ ▓▓▓  ▓    ▓ ▓   ▓ ┃    ┃ ▓▓▓▓▓▓▓      ▓▓▓▓▓▓    ▓▓      ┃
┃▓ ▓  ▓▓▓ ▓      ▓▓▓▓▓ ▓▓▓▓   ▓ ▓┃    ┃  ▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓▓ ▓▓  ▓  ▓ ▓ ▓▓▓ ▓▓▓  ▓   ▓  ┃    ┃    ▓▓▓         ▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓  ▓   ▓▓▓▓ ▓▓ ▓▓    ▓ ▓▓▓▓   ▓┃    ┃         ▓▓▓▓▓▓▓▓▓▓             ┃
┃   ▓ ▓▓▓ ▓▓▓▓▓ ▓  ▓  ▓      ▓▓ ▓┃    ┃         ▓▓▓▓▓▓                 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃     ▓ ▓ ▓▓ ▓   ▓▓▓▓▓  ▓▓ ▓ ▓   ┃    ┃        ▓▓▓      ▓▓▓▓  ▓▓       ┃
┃▓  ▓ ▓ ▓▓▓ ▓     ▓ ▓▓▓ ▓▓   ▓  ▓┃    ┃       ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓       ┃
┃▓ ▓▓▓ ▓▓ ▓ ▓  ▓▓▓▓ ▓ ▓ ▓ ▓▓  ▓  ┃    ┃   ▓▓  ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓     ┃
┃   ▓▓  ▓▓▓▓▓ ▓▓   ▓ ▓▓  ▓▓▓▓▓   ┃    ┃   ▓▓  ▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓  ▓ ▓▓  ▓ ▓     ▓ ▓▓▓ ▓   ▓  ┃    ┃▓▓     ▓▓▓▓▓      ▓▓▓░▓▓▓▓▓▓▓   ┃
┃▓     ▓  ▓▓▓   ▓ ▓▓▓▓   ▓▓▓▓▓ ▓ ┃    ┃▓▓     ▓▓▓▓▓     ▓▓▓     ▓▓▓▓   ┃
┃▓▓ ▓▓ ▓▓ ▓     ▓ ▓▓▓ ▓▓   ▓▓   ▓┃    ┃   ░░░▓▓▓▓▓      ▓▓▓     ▓▓▓▓   ┃
┃▓ ▓▓ ▓▓   ▓  ▓▓ ▓   ▓  ▓▓ ▓▓▓   ┃    ┃    ░░▓▓▓▓▓  ▓▓▓░░     ▓▓▓▓▓▓   ┃
┃   ▓  ▓▓▓▓  ▓▓▓  ▓  ▓▓ ▓▓▓▓ ▓ ▓ ┃    ┃     ▓▓▓▓▓▓ ▓▓▓▓░░     ▓▓▓▓▓▓   ┃
┃ ▓   ▓ ▓ ▓▓ ▓▓▓▓▓ ▓▓   ▓▓ ▓▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓ ▓▓▓▓░░▓▓▓  ▓▓▓▓▓▓   ┃
┃▓   ▓▓   ▓▓  ▓ ▓ ▓▓▓▓ ▓ ▓▓     ▓┃    ┃    ▓▓   ▓▓  ▓▓▓░░▓▓▓▓▓▓▓▓▓     ┃
┃▓▓ ▓▓▓▓ ▓  ▓  ▓▓  ▓ ▓▓▓▓▓ ▓▓▓  ▓┃    ┃   ▓▓▓       ▓▓▓  ▓▓▓▓▓▓▓▓      ┃
┃▓  ▓▓ ▓  ▓ ▓ ▓▓   ▓ ▓ ▓ ▓   ▓   ┃    ┃   ▓▓▓     ▓▓▓▓▓    ▓▓▓▓        ┃
┃   ▓   ▓   ▓▓▓▓▓   ▓  ▓  ▓   ▓ ▓┃    ┃   ▓▓▓     ▓▓▓▓     ▓▓▓         ┃
┃ ▓ ▓▓▓ ▓▓▓  ▓   ▓▓  ▓ ▓▓    ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓ ▓▓▓  ▓▓   ▓▓      ▓▓ ┃
┃  ▓▓ ▓ ▓ ▓ ▓▓▓  ▓▓▓  ▓       ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓ ▓▓   ▓▓▓   ▓      ▓▓ ┃
┃▓ ▓   ▓▓▓▓ ▓   ▓▓ ▓ ▓▓▓▓▓ ▓    ▓┃    ┃     ▓▓▓▓▓░▓▓   ▓▓▓   ▓▓▓       ┃
┃     ▓▓ ▓▓ ▓ ▓   ▓▓   ▓ ▓  ▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓       ┃
┃ ▓ ▓ ▓   ▓ ▓▓▓  ▓  ▓    ▓▓ ▓    ┃    ┃     ▓▓▓▓▓▓▓▓▓  ▓▓▓    ▓▓▓▓▓    ┃
┃▓ ▓  ▓▓▓ ▓ ▓  ▓▓ ▓▓ ▓  ▓▓▓▓▓ ▓ ▓┃    ┃     ▓▓▓▓▓▓▓▓▓  ▓▓▓    ▓▓▓▓▓    ┃
┃▓▓▓ ▓▓▓▓▓   ▓▓  ▓▓   ▓▓▓ ▓  ▓ ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓░▓▓▓▓▓▓▓    ▓▓▓▓▓▓    ┃
┃  ▓▓ ▓   ▓ ▓ ▓ ▓▓ ▓  ▓ ▓  ▓▓    ┃    ┃▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓   ▓▓▓▓▓▓▓    ┃
┃▓▓ ▓  ▓▓▓ ▓▓ ▓▓ ▓  ▓▓  ▓▓▓▓   ▓ ┃    ┃▓▓▓▓▓▓▓▓░░░░░▓▓▓▓   ▓▓▓▓▓▓▓▓    ┃
┃▓▓ ▓ ▓▓  ▓ ▓   ▓▓▓  ▓▓▓▓▓  ▓▓▓  ┃    ┃▓▓▓▓▓▓▓      ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓   ▓▓   ▓   ▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓  ▓▓┃    ┃ ▓▓▓▓▓▓      ▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓  ▓  ▓▓▓▓▓  ▓▓▓▓  ▓ ▓▓▓ ┃    ┃  ▓▓▓▓▓      ▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓   ▓ ▓▓ ▓    ▓ ▓ ▓▓▓   ▓  ▓▓▓▓▓┃    ┃    ▓▓▓       ▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓  ▓ ▓ ▓  ▓  ▓ ▓  ▓ ▓ ▓ ▓▓▓ ▓▓▓┃    ┃              ▓▓▓         ▓▓▓▓▓▓┃
┃ ▓▓  ▓  ▓ ▓  ▓▓▓ ▓   ▓  ▓ ▓▓ ▓ ▓┃    ┃ ▓▓          ▓▓▓          ▓▓▓▓▓▓┃
┃ ▓▓▓  ▓▓  ▓ ▓▓▓▓  ▓▓▓       ▓▓▓▓┃    ┃ ▓▓          ▓▓▓  ▓▓▓▓      ▓▓▓▓┃
┃▓▓ ▓ ▓ ▓▓  ▓  ▓▓  ▓ ▓▓▓ ▓▓  ▓▓▓▓┃    ┃ ▓▓          ▓▓▓  ▓▓▓▓▓▓▓   ▓▓▓▓┃
┃▓ ▓   ▓▓     ▓ ▓  ▓▓▓▓▓▓▓   ▓▓ ▓┃    ┃                  ▓▓▓▓▓▓▓   ▓▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃    ▓▓   ▓▓   ▓   ▓ ▓▓▓▓  ▓▓▓ ▓ ┃    ┃                   ▓▓▓▓   ▓▓▓▓  ┃
┃▓ ▓▓▓  ▓ ▓ ▓▓ ▓  ▓ ▓▓ ▓ ▓ ▓ ▓▓▓ ┃    ┃            ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓ ▓   ▓  ▓ ▓▓  ▓ ▓▓ ▓▓ ▓▓  ▓ ▓┃    ┃           ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃     ▓▓ ▓ ▓ ▓▓▓▓▓▓  ▓ ▓▓   ▓▓▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ┃
┃▓   ▓▓ ▓▓▓▓▓▓ ▓ ▓ ▓▓ ▓ ▓▓   ▓   ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓   ┃
┃ ▓  ▓▓▓  ▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓  ▓▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓   ┃
┃ ▓▓  ▓ ▓ ▓ ▓▓▓ ▓  ▓ ▓▓ ▓▓▓▓ ▓▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓░░░▓▓▓▓┃
┃▓▓ ▓ ▓▓▓  ▓ ▓      ▓▓▓▓▓   ▓ ▓▓▓┃    ┃▓▓░ ▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓░░░▓▓▓▓┃
┃▓  ▓▓   ▓▓ ▓▓         ▓▓▓ ▓▓    ┃    ┃▓▓      ▓▓▓▓▓        ▓▓▓▓░      ┃
┃▓▓▓  ▓  ▓▓▓▓▓▓▓ ▓▓  ▓▓▓  ▓ ▓▓   ┃    ┃▓▓      ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓       ┃
┃        ▓  ▓▓ ▓▓▓▓    ▓▓▓▓   ▓  ┃    ┃          ▓▓▓▓▓▓▓▓   ▓▓▓▓       ┃
┃  ▓▓ ▓▓▓  ▓▓▓▓▓▓   ▓ ▓ ▓   ▓    ┃    ┃   ▓▓▓▓▓  ▓▓▓▓▓▓▓               ┃
┃   ▓▓▓ ▓ ▓▓ ▓ ▓ ▓   ▓        ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓░               ┃
┃  ▓  ▓▓▓ ▓▓▓   ▓ ▓   ▓▓ ▓  ▓▓   ┃    ┃    ▓▓▓▓▓▓▓   ▓░░   ▓▓     ▓▓   ┃
┃ ▓  ▓▓ ▓▓     ▓▓▓▓▓▓▓▓  ▓  ▓▓  ▓┃    ┃    ▓▓▓▓▓     ▓▓▓▓▓▓▓▓     ▓▓   ┃
┃ ▓ ▓ ▓▓ ▓  ▓ ▓ ▓ ▓ ▓   ▓▓▓▓ ▓▓▓▓┃    ┃    ▓▓▓▓▓     ▓▓▓▓▓        ▓▓▓▓▓┃
┃▓   ▓ ▓▓▓▓▓▓   ▓ ▓     ▓  ▓ ▓▓▓ ┃    ┃    ▓▓▓▓▓▓    ▓▓▓▓          ▓▓▓▓┃
┃▓ ▓▓▓ ▓    ▓  ▓▓▓▓   ▓        ▓▓┃    ┃    ▓▓▓▓▓▓    ▓▓▓▓          ▓▓▓▓┃
┃   ▓   ▓▓▓▓  ▓▓ ▓  ▓ ▓    ▓ ▓▓▓▓┃    ┃    ▓▓▓▓▓▓░░▓▓▓▓▓           ▓▓▓▓┃
┃▓   ▓▓▓▓▓▓ ▓ ▓▓ ▓  ▓ ▓▓  ▓ ▓  ▓▓┃    ┃    ▓▓▓▓▓▓░░▓▓▓    ▓▓▓▓     ▓▓▓▓┃
┃    ▓▓ ▓▓  ▓▓▓   ▓ ▓▓ ▓▓▓▓▓ ▓▓▓▓┃    ┃    ▓▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓▓▓      ▓▓ ▓ ▓  ▓  ▓  ▓  ▓┃    ┃    ▓▓▓▓▓               ▓▓▓    ▓┃
┃  ▓▓    ▓▓▓▓▓ ▓   ▓▓▓   ▓▓▓    ▓┃    ┃      ▓▓▓▓▓▓            ▓▓▓    ▓┃
┃     ▓▓ ▓ ▓     ▓    ▓   ▓▓▓▓  ▓┃    ┃      ▓▓▓▓▓▓            ▓▓▓▓▓  ▓┃
┃▓▓ ▓▓ ▓▓  ▓▓   ▓▓  ▓ ▓▓▓▓▓  ▓▓▓▓┃    ┃▓▓▓▓▓▓▓               ▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓   ▓       ▓ ▓ ▓    ▓▓ ▓  ┃    ┃▓▓▓▓▓▓▓              ▓▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓▓▓▓   ▓▓ ▓▓ ▓    ▓▓ ▓ ▓    ┃    ┃▓▓▓▓▓▓▓      ▓▓▓     ▓▓▓▓▓▓░    ┃
┃▓▓  ▓▓▓  ▓▓  ▓▓▓    ▓▓▓▓▓▓▓   ▓ ┃    ┃▓▓  ▓▓▓▓  ▓▓▓▓▓▓    ▓▓▓▓▓▓░░    ┃
┃    ▓ ▓▓▓ ▓▓▓▓ ▓▓▓▓ ▓▓ ▓ ▓ ▓  ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░    ┃
┃  ▓     ▓ ▓ ▓▓▓▓ ▓▓▓  ▓    ▓▓  ▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓░░▓▓   ┃
┃▓▓ ▓  ▓▓▓▓ ▓▓ ▓  ▓▓   ▓▓ ▓ ▓▓ ▓▓┃    ┃▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓░░▓▓   ┃
┃▓▓     ▓▓ ▓▓▓  ▓▓▓▓▓▓▓▓▓▓ ▓▓▓  ▓┃    ┃▓▓     ▓▓▓▓▓▓    ▓▓▓▓▓▓▓░░░▓▓   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓▓  ▓▓▓▓ ▓  ▓ ▓  ▓  ▓   ▓▓▓ ┃    ┃  ▓▓▓    ▓▓                     ┃
┃ ▓ ▓ ▓  ▓ ▓  ▓▓ ▓   ▓▓  ▓ ▓    ▓┃    ┃▓▓▓▓▓    ▓▓  ▓▓                 ┃
┃▓▓▓▓     ▓▓▓ ▓▓▓ ▓▓▓ ▓   ▓    ▓ ┃    ┃▓▓▓▓     ▓▓  ▓▓                 ┃
┃▓    ▓  ▓ ▓     ▓    ▓ ▓▓    ▓ ▓┃    ┃         ▓▓            ▓▓▓      ┃
┃    ▓▓  ▓ ▓   ▓ ▓ ▓ ▓ ▓▓▓▓  ▓   ┃    ┃         ▓▓            ▓▓▓      ┃
┃▓  ▓▓  ▓ ▓▓▓  ▓   ▓  ▓ ▓▓▓  ▓▓▓ ┃    ┃   ▓▓                 ░▓▓▓      ┃
┃▓ ▓▓▓   ▓   ▓▓▓▓▓▓  ▓▓▓  ▓      ┃    ┃   ▓▓     ▓▓▓▓▓▓     ░░░░░      ┃
┃  ▓    ▓  ▓▓ ▓ ▓  ▓▓ ▓ ▓ ▓  ▓ ▓▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓░░░░     ▓▓┃
┃     ▓ ▓  ▓▓▓▓ ▓ ▓▓ ▓   ▓ ▓   ▓▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓         ▓▓┃
┃    ▓ ▓ ▓▓▓  ▓▓ ▓ ▓▓▓▓  ▓▓   ▓ ▓┃    ┃         ▓▓  ▓▓▓▓▓▓▓▓           ┃
┃ ▓▓  ▓▓   ▓  ▓▓ ▓ ▓  ▓ ▓  ▓▓▓▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓          ░▓▓  ┃
┃ ▓▓▓▓▓▓ ▓▓     ▓▓      ▓ ▓ ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓               ░░▓▓  ┃
┃  ▓ ▓ ▓▓▓▓▓ ▓      ▓▓ ▓▓  ▓ ▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓░░░  ┃
┃ ▓▓▓  ▓ ▓ ▓▓▓▓▓▓▓     ▓▓▓▓▓▓    ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓░░░  ┃
┃▓  ▓▓ ▓▓  ▓ ▓ ▓  ▓▓    ▓▓ ▓ ▓ ▓▓┃    ┃ ▓▓▓       ▓▓▓▓▓▓▓▓   ▓▓▓▓▓░░▓▓ ┃
┃ ▓▓      ▓ ▓ ▓▓▓▓▓▓▓  ▓  ▓▓ ▓▓▓ ┃    ┃           ▓▓▓▓▓▓▓▓▓      ░░░▓▓ ┃
┃ ▓  ▓ ▓▓▓  ▓▓▓ ▓▓ ▓▓ ▓ ▓  ▓ ▓   ┃    ┃     ▓▓▓   ▓▓▓▓▓▓▓▓▓      ░░    ┃
┃   ▓ ▓▓▓    ▓ ▓ ▓▓▓▓▓      ▓   ▓┃    ┃     ▓▓▓   ▓▓▓▓▓▓▓▓▓      ░░    ┃
┃ ▓▓  ▓ ▓ ▓▓▓    ▓▓      ▓▓▓▓    ┃    ┃     ▓▓▓▓  ▓▓  ▓▓▓      ▓▓▓▓    ┃
┃▓   ▓ ▓▓▓  ▓▓ ▓ ▓  ▓ ▓ ▓▓  ▓ ▓ ▓┃    ┃     ▓▓▓▓  ▓▓  ▓▓▓      ▓▓▓▓    ┃
┃ ▓ ▓▓▓ ▓▓  ▓▓ ▓▓ ▓▓   ▓ ▓▓  ▓▓▓▓┃    ┃    ▓▓▓▓▓  ▓▓▓▓▓▓░      ▓▓▓▓▓▓▓ ┃
┃ ▓ ▓ ▓  ▓ ▓▓▓ ▓▓▓  ▓ ▓ ▓ ▓▓▓▓  ▓┃    ┃    ▓▓▓▓▓ ▓▓▓▓▓▓░░      ▓▓▓▓▓▓▓ ┃
┃▓    ▓▓▓▓ ▓ ▓▓   ▓     ▓ ▓ ▓ ▓ ▓┃    ┃     ▓▓▓▓ ▓▓▓▓▓▓░       ▓▓▓▓▓▓▓ ┃
┃   ▓      ▓▓▓ ▓ ▓ ▓   ▓ ▓  ▓  ▓ ┃    ┃          ▓▓▓▓▓▓        ░░░░    ┃
┃▓▓▓▓   ▓▓  ▓  ▓ ▓▓▓  ▓ ▓ ▓ ▓   ▓┃    ┃                        ░░░     ┃
┃   ▓▓▓    ▓  ▓▓    ▓▓▓▓   ▓ ▓▓  ┃    ┃   ▓▓              ▓▓▓▓▓░░      ┃
┃▓  ▓  ▓▓▓ ▓    ▓▓  ▓▓▓ ▓ ▓▓ ▓ ▓ ┃    ┃   ▓▓▓▓▓▓     ▓▓▓  ▓▓▓▓▓        ┃
┃▓  ▓▓▓▓▓▓    ▓▓▓▓   ▓▓▓▓   ▓    ┃    ┃   ▓▓▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓        ┃
┃ ▓  ▓ ▓▓▓▓  ▓▓ ▓▓▓ ▓    ▓   ▓▓ ▓┃    ┃   ▓▓▓▓▓▓▓  ▓▓▓▓▓     ▓▓    ▓▓▓ ┃
┃▓ ▓▓▓   ▓▓▓▓▓ ▓ ▓  ▓ ▓▓▓  ▓ ▓▓▓▓┃    ┃   ▓▓  ▓▓▓▓▓▓▓▓▓▓     ▓▓    ▓▓▓▓┃
┃  ▓   ▓▓ ▓   ▓ ▓ ▓ ▓ ▓  ▓  ▓ ▓▓▓┃    ┃        ▓▓▓           ▓▓▓   ▓▓▓▓┃
┃▓   ▓    ▓▓▓  ▓▓▓ ▓   ▓▓▓▓▓▓▓  ▓┃    ┃         ▓▓            ▓▓       ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓▓ ▓ ▓  ▓ ▓▓ ▓  ▓ ▓▓  ▓    ▓▓┃    ┃                     ▓▓         ┃
┃▓ ▓ ▓   ▓ ▓     ▓▓▓▓ ▓▓  ▓  ▓▓▓ ┃    ┃                   ░▓▓▓     ▓▓▓ ┃
┃  ▓▓ ▓▓▓▓▓ ▓   ▓    ▓▓▓▓▓   ▓▓ ▓┃    ┃     ▓▓▓▓▓▓         ▓▓▓▓▓   ▓▓▓ ┃
┃▓▓   ▓  ▓   ▓▓  ▓    ▓ ▓▓▓   ▓▓ ┃    ┃     ▓▓▓▓▓▓         ▓▓▓▓▓    ▓▓ ┃
┃▓  ▓  ▓▓▓▓▓ ▓    ▓ ▓▓ ▓ ▓ ▓  ▓ ▓┃    ┃     ▓▓▓▓▓▓         ▓▓▓▓▓▓   ▓  ┃
┃ ▓▓  ▓▓   ▓▓ ▓▓    ▓ ▓▓ ▓ ▓ ▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓  ┃
┃▓ ▓▓▓▓▓ ▓▓▓     ▓  ▓▓   ▓ ▓▓ ▓  ┃    ┃  ▓▓▓▓▓  ▓▓             ▓▓▓▓▓▓  ┃
┃    ▓ ▓ ▓   ▓▓ ▓  ▓▓  ▓  ▓▓▓ ▓▓ ┃    ┃    ░░                  ▓▓▓▓▓▓▓ ┃
┃▓    ▓    ▓▓   ▓▓  ▓▓ ▓▓▓▓ ▓▓▓▓▓┃    ┃    ░              ░  ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓  ▓▓▓  ▓▓  ▓▓    ▓  ▓▓ ▓ ▓▓▓▓ ┃    ┃         ▓▓▓       ▓  ▓▓▓  ▓▓▓▓ ┃
┃▓ ▓ ▓ ▓  ▓ ▓▓  ▓ ▓ ▓    ▓  ▓  ▓ ┃    ┃         ▓▓▓       ▓   ▓▓  ▓▓▓▓ ┃
┃▓  ▓   ▓ ▓▓▓ ▓ ▓▓▓ ▓▓  ▓▓ ▓▓▓▓ ▓┃    ┃         ▓▓▓    ▓▓ ▓▓      ▓▓▓▓ ┃
┃  ▓ ▓   ▓    ▓  ▓▓ ▓▓ ▓▓  ▓ ▓ ▓▓┃    ┃                ▓▓ ▓▓▓     ▓▓▓▓▓┃
┃ ▓   ▓  ▓ ▓ ▓▓   ▓  ▓▓     ▓▓▓▓▓┃    ┃            ▓▓  ▓▓  ▓▓      ▓▓▓▓┃
┃ ▓▓▓ ▓  ▓ ▓ ▓▓▓▓ ▓   ▓ ▓▓   ▓  ▓┃    ┃ ▓▓     ▓▓▓▓▓▓▓▓▓▓  ▓▓       ▓▓▓┃
┃▓ ▓ ▓  ▓▓ ▓▓ ▓▓ ▓▓ ▓▓▓▓  ▓  ▓ ▓▓┃    ┃ ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓          ┃
┃  ▓      ▓    ▓▓▓  ▓▓▓  ▓▓ ▓    ┃    ┃ ▓▓          ▓▓▓▓▓▓▓▓▓          ┃
┃▓▓▓ ▓▓▓ ▓    ▓▓  ▓▓  ▓ ▓      ▓▓┃    ┃    ▓▓▓      ▓▓▓▓▓▓             ┃
┃ ▓  ▓▓ ▓     ▓▓▓▓▓▓  ▓▓    ▓▓   ┃    ┃    ▓▓▓      ▓▓▓▓▓▓             ┃
┃▓  ▓▓▓▓▓ ▓▓▓ ▓    ▓▓▓  ▓▓     ▓▓┃    ┃    ▓▓▓    ▓▓▓  ▓▓▓▓▓           ┃
┃ ▓     ▓    ▓▓ ▓▓▓▓▓▓  ▓ ▓▓▓▓   ┃    ┃          ▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓▓   ┃
┃  ▓▓ ▓   ▓ ▓▓▓   ▓   ▓▓▓ ▓▓ ▓▓  ┃    ┃          ▓▓▓▓    ░░▓▓▓▓▓▓▓▓▓   ┃
┃ ▓  ▓▓ ▓▓ ▓▓  ▓ ▓ ▓ ▓ ▓ ▓    ▓▓ ┃    ┃ ▓▓▓▓     ▓▓▓     ░▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓ ▓   ▓▓  ▓  ▓  ▓  ▓▓▓ ▓▓ ▓ ▓┃    ┃ ▓▓▓▓▓   ▓▓▓▓     ▓▓▓▓▓▓▓▓▓     ┃
┃▓▓▓▓▓▓▓▓▓ ▓▓▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓  ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓     ┃
┃  ▓   ▓ ▓▓ ▓     ▓▓▓▓▓ ▓▓▓▓   ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓     ┃
┃ ▓ ▓▓▓▓▓  ▓▓ ▓▓▓  ▓   ▓▓  ▓   ▓ ┃    ┃ ▓▓▓▓▓▓   ▓▓      ▓▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓▓    ▓▓▓      ▓▓▓▓   ▓▓▓▓ ▓▓┃    ┃ ▓▓▓▓▓▓   ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃   ▓ ▓ ▓   ▓ ▓ ▓ ▓▓ ▓▓ ▓▓▓▓▓▓▓ ▓┃    ┃  ▓▓▓▓    ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓ ▓▓  ▓▓▓▓   ▓ ▓ ▓ ▓ ▓▓  ▓▓▓▓┃    ┃  ▓▓▓▓   ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓  ▓▓▓▓▓▓  ▓ ▓  ▓▓▓ ▓▓▓▓▓ ▓┃    ┃  ▓▓▓▓   ▓▓▓▓   ▓▓    ▓▓▓▓▓▓▓▓▓▓┃
┃▓   ▓    ▓  ▓   ▓▓  ▓ ▓▓  ▓▓▓▓▓▓┃    ┃                      ▓▓  ▓▓▓▓▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓ ▓      ▓▓▓  ▓ ▓▓ ▓   ▓▓  ▓ ┃    ┃  ▓▓                      ▓▓    ┃
┃▓▓▓▓    ▓   ▓   ▓▓▓ ▓ ▓▓▓▓▓▓▓▓ ▓┃    ┃▓▓▓▓              ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓  ▓ ▓  ▓   ▓▓▓  ▓▓ ▓  ▓   ▓  ┃    ┃▓▓▓▓             ▓▓▓▓▓▓     ▓▓  ┃
┃  ▓▓▓ ▓▓    ▓ ▓ ▓ ▓▓ ▓▓    ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓         ▓▓▓▓▓      ▓▓  ┃
┃ ▓▓ ▓ ▓▓▓▓     ▓ ▓ ▓▓    ▓ ▓▓▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓      ░▓▓▓        ▓▓▓ ┃
┃     ▓ ▓ ▓▓ ▓▓▓   ▓▓  ▓▓▓▓  ▓▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓▓░░▓▓▓  ▓▓▓▓  ▓▓▓ ┃
┃▓   ▓      ▓▓  ▓ ▓▓▓  ▓▓  ▓  ▓  ┃    ┃          ▓▓▓▓▓  ▓▓▓  ▓▓▓▓  ▓▓▓ ┃
┃  ▓ ▓  ▓  ▓▓ ▓▓  ▓▓▓ ▓▓ ▓▓ ▓▓▓▓▓┃    ┃          ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓ ▓▓▓ ▓ ▓▓▓ ▓  ▓  ▓▓▓ ▓ ▓▓▓▓▓▓┃    ┃   ▓▓▓    ▓▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓ ▓▓       ▓ ▓ ▓▓     ▓▓ ▓  ▓ ┃    ┃   ▓▓▓    ▓▓▓▓▓               ▓ ┃
┃ ▓ ▓ ▓  ▓▓▓▓▓▓▓ ▓▓    ▓       ▓ ┃    ┃         ▓▓▓▓▓▓▓▓             ▓ ┃
┃▓      ▓ ▓  ▓ ▓       ▓ ▓▓    ▓▓┃    ┃         ▓▓▓▓▓▓▓▓             ▓▓┃
┃▓ ▓ ▓    ▓▓▓  ▓▓▓   ▓ ▓▓ ▓    ▓▓┃    ┃▓▓       ▓▓▓▓▓▓▓▓    ▓▓▓▓▓    ▓▓┃
┃▓▓ ▓ ▓ ▓  ▓▓▓ ▓▓▓▓▓▓▓▓  ▓▓▓▓ ▓▓ ┃    ┃▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓▓┃
┃▓▓   ▓  ▓▓ ▓▓ ▓ ▓▓   ▓  ▓    ▓▓▓┃    ┃▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓  ▓▓▓┃
┃ ▓ ▓▓▓ ▓ ▓▓▓ ▓ ▓     ▓ ▓▓▓▓    ▓┃    ┃ ▓  ▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓▓    ▓┃
┃ ▓   ▓▓▓▓▓▓▓ ▓▓▓  ▓  ▓▓ ▓▓▓▓▓  ▓┃    ┃ ▓  ▓▓▓▓▓▓▓▓▓▓▓▓       ░▓▓▓▓   ▓┃
┃▓▓▓▓▓ ▓ ▓ ▓  ▓ ▓  ▓  ▓ ▓  ▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ░░  ▓▓▓▓▓┃
┃▓   ▓▓▓▓▓▓▓▓ ▓ ▓   ▓▓   ▓  ▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ░░   ▓▓▓▓┃
┃▓▓▓▓▓    ▓ ▓▓▓ ▓       ▓ ▓  ▓ ▓▓┃    ┃▓▓▓▓▓    ▓▓▓▓▓▓▓       ░░   ▓▓▓▓┃
┃▓▓  ▓     ▓  ▓ ▓▓▓   ▓▓▓▓▓▓ ▓   ┃    ┃▓▓       ▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓┃
┃     ▓▓▓▓▓ ▓▓ ▓    ▓▓▓▓▓▓▓▓▓ ▓▓▓┃    ┃          ▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓    ▓ ▓ ▓ ▓ ▓▓  ▓   ▓▓▓▓▓▓▓▓┃    ┃            ░▓░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓  ▓ ▓      ▓ ▓ ▓▓▓▓ ▓ ▓       ┃    ┃            ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃▓  ▓▓▓ ▓    ▓ ▓ ▓▓▓▓ ▓▓▓ ▓▓   ▓▓┃    ┃    ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓┃
┃  ▓ ▓▓▓    ▓  ▓▓▓▓ ▓▓▓▓▓▓ ▓ ▓▓▓▓┃    ┃    ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓▓▓   ▓▓▓▓▓▓ ▓▓ ▓  ▓▓▓▓▓▓▓   ┃    ┃    ▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓      ▓▓ ▓▓▓▓ ▓▓ ▓▓▓  ▓▓▓▓▓ ▓▓▓┃    ┃         ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓▓   ▓▓ ▓▓▓   ▓▓▓  ▓▓  ▓▓▓▓▓▓┃    ┃         ▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓▓▓┃
┃ ▓ ▓ ▓▓ ▓ ▓   ▓▓  ▓▓  ▓▓▓▓  ▓▓ ▓┃    ┃  ▓▓     ▓▓▓▓▓▓▓  ▓▓  ▓▓▓   ▓▓▓▓┃
┃ ▓▓▓▓ ▓  ▓▓ ▓▓▓▓   ▓▓ ▓▓    ▓▓ ▓┃    ┃  ▓▓     ▓▓  ▓▓▓      ▓▓▓   ▓▓  ┃
┃        ▓▓▓ ▓  ▓ ▓ ▓ ▓  ▓▓   ▓  ┃    ┃         ▓▓                     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓      ▓ ▓▓ ▓▓ ▓ ▓   ▓▓▓▓▓▓▓▓▓▓┃    ┃          ▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓ ▓▓ ▓  ▓▓▓▓▓     ▓ ▓▓▓ ▓ ▓▓  ┃    ┃    ▓▓    ▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓▓▓   ▓ ▓ ▓   ▓▓▓▓  ▓▓▓    ▓▓┃    ┃    ▓▓     ▓▓▓         ▓▓▓▓   ▓▓┃
┃▓ ▓  ▓▓▓     ▓ ▓        ▓▓▓   ▓▓┃    ┃     ▓▓▓               ▓▓▓▓   ▓▓┃
┃  ▓  ▓ ▓ ▓ ▓▓   ▓ ▓▓▓▓ ▓▓ ▓   ▓ ┃    ┃     ▓▓▓   ▓▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓┃
┃  ▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓ ▓▓  ▓▓▓▓ ▓▓▓▓▓┃    ┃  ▓▓▓▓▓▓ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓    ▓▓▓▓▓▓ ▓   ▓▓ ▓   ▓▓▓ ▓┃    ┃  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓┃
┃   ▓▓ ▓   ▓   ▓▓▓▓▓▓ ▓    ▓▓▓  ▓┃    ┃  ▓▓▓▓       ▓▓▓▓░▓▓▓▓    ▓▓▓   ┃
┃ ▓▓  ▓▓▓     ▓▓▓▓   ▓▓▓   ▓▓▓  ▓┃    ┃   ▓▓▓▓      ▓▓▓▓  ▓▓▓    ▓▓▓   ┃
┃ ▓ ▓▓  ▓  ▓▓▓ ▓    ▓▓▓ ▓▓ ▓  ▓  ┃    ┃   ▓▓▓▓      ▓▓▓   ▓▓▓▓▓▓▓▓▓    ┃
┃    ▓▓▓ ▓▓   ▓ ▓▓   ▓▓ ▓▓  ▓  ▓ ┃    ┃   ▓▓▓▓▓▓▓▓░░▓▓▓   ▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓▓   ▓▓▓▓ ▓▓▓▓ ▓ ▓▓▓  ▓▓▓ ▓ ▓▓┃    ┃       ▓▓▓▓░░▓▓▓  ▓▓▓▓▓▓▓▓▓▓    ┃
┃   ▓ ▓  ▓  ▓     ▓▓   ▓▓ ▓▓    ▓┃    ┃       ▓▓▓▓░░    ▓▓▓   ▓▓▓▓▓    ┃
┃▓▓▓    ▓▓▓▓▓▓    ▓▓▓    ▓  ▓▓  ▓┃    ┃       ▓▓▓▓░░    ▓▓▓   ▓▓▓▓▓▓   ┃
┃ ▓ ▓   ▓▓▓▓  ▓   ▓▓▓ ▓▓▓▓▓ ▓▓▓▓ ┃    ┃▓▓▓▓   ▓▓▓▓░░    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓▓▓▓ ▓  ▓▓▓   ▓▓▓▓ ▓  ▓  ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓▓ ▓     ▓ ▓  ▓▓▓▓▓ ▓▓ ▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓     ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓ ▓  ▓   ▓ ▓▓    ▓ ▓  ▓ ▓    ▓┃    ┃  ▓▓▓       ▓▓▓   ▓▓▓▓        ▓ ┃
┃▓  ▓▓      ▓▓ ▓▓  ▓▓ ▓  ▓ ▓ ▓▓ ▓┃    ┃  ▓▓▓      ▓▓▓▓▓  ▓▓▓▓        ▓▓┃
┃ ▓▓▓    ▓  ▓▓ ▓▓  ▓ ▓▓▓ ▓     ▓▓┃    ┃▓▓▓▓▓      ▓▓▓▓▓   ▓▓▓        ▓▓┃
┃▓▓  ▓ ▓ ▓ ▓▓▓▓  ▓   ▓      ▓▓ ▓ ┃    ┃▓▓▓▓▓    ▓▓▓▓      ▓▓▓          ┃
┃▓ ▓▓▓ ▓  ▓▓▓▓   ▓  ▓▓ ▓    ▓ ▓  ┃    ┃ ▓▓▓     ▓▓▓▓      ▓▓▓     ▓▓▓  ┃
┃ ▓▓ ▓ ▓  ▓▓▓▓ ▓ ▓  ▓ ▓ ▓▓▓ ▓ ▓▓ ┃    ┃ ▓▓▓     ▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓   ▓   ▓ ▓  ▓ ▓▓▓▓▓▓▓▓▓▓▓▓ ▓ ┃    ┃ ▓▓       ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃   ▓     ▓  ▓▓ ▓▓▓▓       ▓▓    ┃    ┃           ▓▓  ▓▓▓▓▓    ▓▓▓▓    ┃
┃ ▓▓  ▓▓    ▓▓  ▓▓ ▓▓  ▓ ▓▓ ▓    ┃    ┃           ▓▓  ▓▓▓▓▓    ▓▓▓▓    ┃
┃  ▓        ▓▓  ▓▓▓ ▓▓ ▓▓ ▓▓▓ ▓▓▓┃    ┃           ▓▓  ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓ ┃
┃▓   ▓ ▓▓   ▓▓▓ ▓▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓┃    ┃           ▓▓▓ ▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓ ┃
┃  ▓ ▓  ▓   ▓▓▓  ▓▓ ▓▓ ▓ ▓   ▓ ▓ ┃    ┃           ▓▓▓  ▓▓▓▓▓ ▓▓▓▓  ▓▓▓ ┃
┃  ▓ ▓  ▓     ▓   ▓ ▓  ▓ ▓▓  ▓  ▓┃    ┃                ▓▓          ▓▓▓ ┃
┃▓ ▓       ▓  ▓▓ ▓▓    ▓     ▓▓▓▓┃    ┃                ▓▓          ▓▓  ┃
┃  ▓ ▓▓▓ ▓  ▓  ▓ ▓  ▓ ▓ ▓▓▓ ▓ ▓ ▓┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓ ▓▓▓ ▓▓▓▓▓▓ ▓▓▓   ▓▓▓  ▓▓  ▓┃    ┃  ▓▓▓▓▓▓▓░▓▓▓▓             ▓▓   ┃
┃▓ ▓▓▓  ▓▓ ▓▓ ▓ ▓  ▓▓     ▓ ▓▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓            ▓▓▓▓  ┃
┃▓ ▓ ▓ ▓▓ ▓▓ ▓▓      ▓ ▓  ▓▓ ▓▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓ ┃
┃▓  ▓ ▓▓▓▓ ▓ ▓▓ ▓▓▓ ▓  ▓▓▓▓▓▓  ▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓  ▓▓┃
┃ ▓▓▓ ▓ ▓   ▓ ▓   ▓▓  ▓▓ ▓▓▓▓  ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓░░░▓▓▓▓▓▓  ▓▓┃
┃▓▓▓  ▓ ▓▓▓ ▓  ▓ ▓ ▓▓ ▓    ▓ ▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓░░░▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓▓▓  ▓ ▓▓ ▓ ▓    ▓ ▓▓ ▓▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓░        ▓▓▓▓▓▓▓▓▓▓┃
┃    ▓ ▓▓ ▓▓  ▓▓   ▓ ▓ ▓▓ ▓ ▓▓▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓░░        ▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓ ▓▓▓▓▓ ▓▓ ▓  ▓▓       ▓   ▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓          ▓   ▓▓▓┃
┃   ▓▓▓ ▓  ▓▓ ▓▓▓ ▓▓ ▓ ▓ ▓▓     ▓┃    ┃    ▓▓▓   ▓▓▓▓▓          ▓    ░░┃
┃▓▓  ▓    ▓ ▓  ▓ ▓   ▓    ▓▓  ▓ ▓┃    ┃▓▓  ▓     ░░▓▓▓          ▓▓   ░░┃
┃▓▓▓ ▓   ▓   ▓▓ ▓         ▓▓▓  ▓ ┃    ┃▓▓▓▓▓     ░░░░           ▓▓▓  ░░┃
┃▓ ▓ ▓▓▓▓▓▓▓▓ ▓     ▓ ▓▓ ▓▓ ▓▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓░           ▓▓▓▓▓▓▓┃
┃▓ ▓▓   ▓▓▓    ▓  ▓▓▓▓   ▓   ▓▓▓ ┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓       ▓▓▓▓┃
┃▓ ▓   ▓  ▓ ▓▓▓▓▓   ▓▓     ▓   ▓▓┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓        ▓▓▓┃
┃▓▓▓▓▓ ▓▓▓▓▓▓     ▓   ▓▓   ▓ ▓▓ ▓┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓                  ┃
┃▓ ▓   ▓    ▓ ▓▓ ▓▓ ▓ ▓ ▓ ▓ ▓  ▓ ┃    ┃      ▓    ▓▓▓▓▓▓▓▓  ▓▓         ┃
┃   ▓  ▓     ▓▓▓▓ ▓▓▓ ▓▓      ▓ ▓┃    ┃      ▓    ▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓    ▓▓▓▓▓ ▓   ▓▓  ▓▓ ▓ ▓   ▓▓  ┃    ┃     ▓▓       ▓▓▓▓▓▓▓           ┃
┃  ▓▓▓▓▓   ▓▓ ▓▓▓ ▓▓  ▓     ▓ ▓  ┃    ┃  ▓▓▓▓▓    ░  ▓▓▓▓▓▓        ▓▓  ┃
┃ ▓▓▓ ▓▓  ▓     ▓  ▓▓   ▓ ▓▓▓ ▓▓ ┃    ┃  ▓▓▓▓▓   ░░  ▓▓▓▓░        ▓▓▓▓ ┃
┃  ▓   ▓  ▓▓▓▓▓ ▓ ▓  ▓  ▓    ▓ ▓▓┃    ┃     ▓▓  ▓▓▓▓▓▓▓▓░░       ▓▓▓▓▓ ┃
┃▓    ▓▓▓ ▓▓  ▓ ▓▓ ▓ ▓▓   ▓ ▓▓ ▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓▓░░▓▓      ▓▓▓▓▓ ┃
┃  ▓   ▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓   ▓▓ ▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓░░▓▓▓     ▓▓▓▓▓ ┃
┃▓▓▓▓▓ ▓▓ ▓ ▓ ▓▓ ▓ ▓▓ ▓▓▓▓ ▓▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓   ▓▓▓▓▓ ┃
┃▓ ▓▓▓▓     ▓▓▓▓  ▓▓ ▓▓▓    ▓▓▓ ▓┃    ┃▓▓▓▓▓▓    ▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓ ┃
┃▓ ▓ ▓▓  ▓ ▓▓ ▓ ▓  ▓▓▓▓    ▓   ▓ ┃    ┃▓▓▓▓▓▓    ▓▓▓▓▓   ▓▓▓▓    ▓▓▓▓  ┃
┃▓▓▓   ▓ ▓ ▓▓▓▓▓▓▓  ▓    ▓▓ ▓▓ ▓▓┃    ┃▓▓▓       ▓▓▓▓▓           ░     ┃
┃▓ ▓  ▓    ▓▓▓▓   ▓   ▓ ▓  ▓ ▓▓  ┃    ┃          ▓▓▓▓▓                 ┃
┃   ▓ ▓ ▓▓ ▓  ▓▓   ▓    ▓▓ ▓     ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓         ▓▓▓     ┃
┃   ▓▓▓▓ ▓▓ ▓▓ ▓ ▓ ▓▓   ▓ ▓▓  ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓  ▓▓     ▓▓▓     ┃
┃      ▓▓   ▓▓▓▓ ▓▓▓ ▓  ▓ ▓▓    ▓┃    ┃           ▓▓▓▓  ▓▓      ▓▓     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓   ▓▓ ▓▓         ▓▓   ▓▓   ▓   ┃    ┃                  ▓▓            ┃
┃ ▓▓▓ ▓▓  ▓▓▓▓   ▓ ▓▓  ▓   ▓▓▓▓  ┃    ┃     ▓▓   ▓▓      ▓▓        ▓▓  ┃
┃▓    ▓  ▓ ▓   ▓   ▓▓ ▓  ▓▓  ▓▓▓ ┃    ┃    ▓▓▓   ▓▓      ▓▓▓       ▓▓  ┃
┃▓▓ ▓▓▓▓▓ ▓▓▓▓  ▓▓  ▓▓▓ ▓  ▓ ▓▓ ▓┃    ┃    ▓▓▓   ▓▓    ▓▓▓▓▓▓      ▓▓  ┃
┃▓   ▓ ▓    ▓  ▓ ▓▓▓▓▓▓   ▓▓ ▓▓  ┃    ┃    ▓▓          ▓▓▓▓▓▓     ▓▓▓▓ ┃
┃   ▓▓▓        ▓   ▓▓▓ ▓ ▓▓    ▓▓┃    ┃   ▓▓▓          ▓▓▓▓▓▓     ▓▓▓▓ ┃
┃    ▓  ▓ ▓▓▓▓ ▓ ▓▓ ▓ ▓▓  ▓ ▓▓▓▓ ┃    ┃   ▓▓▓          ▓▓▓▓▓▓    ▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓▓ ▓     ▓▓▓▓   ▓▓ ▓▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓        ▓▓▓▓▓    ▓▓▓▓▓  ┃
┃ ▓▓ ▓▓▓     ▓▓▓ ▓▓▓▓▓   ▓  ▓    ┃    ┃ ▓▓▓▓▓▓▓        ▓▓▓▓▓   ▓▓▓▓▓▓  ┃
┃▓▓▓ ▓  ▓▓▓   ▓    ▓▓▓▓▓ ▓▓▓ ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃   ▓▓ ▓ ▓▓▓▓▓   ▓  ▓▓  ▓ ▓  ▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓▓▓ ▓   ▓     ▓▓ ▓ ▓ ▓▓▓▓  ▓▓┃    ┃ ▓▓▓▓▓▓░          ▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓   ▓    ▓    ▓ ▓ ▓▓▓▓▓ ▓ ▓   ┃    ┃ ▓▓▓▓▓▓▓            ▓▓▓▓▓▓▓     ┃
┃  ▓ ▓▓▓▓▓ ▓ ▓▓ ▓     ▓ ▓▓      ▓┃    ┃ ▓▓▓▓▓▓▓▓▓           ▓▓▓▓       ┃
┃▓ ▓▓▓▓▓ ▓▓    ▓    ▓▓ ▓   ▓     ┃    ┃ ▓▓▓▓▓▓▓▓▓           ▓▓▓        ┃
┃▓▓ ▓ ▓  ▓▓ ▓ ▓ ▓      ▓▓  ▓▓▓ ▓▓┃    ┃ ▓▓▓    ▓▓           ▓▓▓        ┃
┃ ▓▓     ▓▓   ▓▓    ▓▓▓ ▓ ▓     ▓┃    ┃ ▓▓     ▓▓           ▓▓▓        ┃
┃  ▓▓      ▓  ▓  ▓▓   ▓▓        ▓┃    ┃                     ░          ┃
┃    ▓▓ ▓    ▓  ▓▓ ▓▓ ▓ ▓  ▓ ▓▓  ┃    ┃                ▓▓░░░           ┃
┃       ▓▓▓▓     ▓ ▓ ▓ ▓ ▓    ▓ ▓┃    ┃       ▓▓▓      ▓▓░░            ┃
┃▓▓▓▓  ▓▓ ▓ ▓▓ ▓ ▓▓ ▓▓ ▓ ▓   ▓ ▓ ┃    ┃▓▓▓   ▓▓▓▓▓   ▓▓▓▓              ┃
┃▓▓  ▓▓▓▓▓▓▓  ▓▓▓▓▓▓     ▓ ▓ ▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓         ▓▓▓  ┃
┃▓ ▓▓▓▓▓ ▓ ▓  ▓▓▓      ▓▓ ▓ ▓▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓     ▓▓ ░▓▓▓  ┃
┃▓     ▓▓▓ ▓     ▓▓▓▓▓▓ ▓▓▓ ▓ ▓ ▓┃    ┃▓▓   ▓▓▓▓▓▓          ░▓▓▓       ┃
┃▓ ▓  ▓ ▓▓ ▓ ▓      ▓ ▓        ▓▓┃    ┃▓▓   ▓▓▓▓▓▓▓                    ┃
┃▓▓▓  ▓▓▓▓▓▓▓▓  ▓ ▓     ▓▓▓ ▓▓  ▓┃    ┃▓▓▓  ▓▓▓▓▓▓▓                    ┃
┃▓▓▓ ▓  ▓▓     ▓▓      ▓   ▓▓  ▓ ┃    ┃▓▓▓  ▓▓▓▓▓▓               ▓▓    ┃
┃ ▓  ▓▓▓▓▓▓▓▓ ▓   ▓▓ ▓▓▓ ▓  ▓   ▓┃    ┃▓▓▓  ▓▓▓▓▓▓      ▓▓░░▓▓▓  ▓▓  ░ ┃
┃▓▓▓  ▓▓▓▓▓      ▓▓▓▓  ▓▓  ▓▓▓▓▓▓┃    ┃ ▓▓  ▓▓▓▓▓▓      ▓▓░░▓▓▓  ▓▓▓▓▓▓┃
┃  ▓▓ ▓  ▓▓ ▓▓▓   ▓  ▓▓▓▓ ▓▓▓ ▓ ▓┃    ┃     ▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓ ▓ ▓▓▓▓  ▓▓     ▓▓▓▓▓▓ ▓  ▓┃    ┃        ▓▓▓▓  ▓▓     ▓▓▓▓▓▓▓    ┃
┃   ▓  ▓    ▓ ▓▓▓▓       ▓ ▓▓    ┃    ┃              ▓▓         ▓▓     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓    ▓ ▓▓▓▓▓▓▓▓▓▓ ▓ ▓  ▓ ▓  ▓ ┃    ┃ ▓▓         ▓▓▓▓                ┃
┃▓▓▓   ▓▓ ▓ ▓  ▓▓   ▓▓▓ ▓    ▓  ▓┃    ┃ ▓▓   ▓▓    ▓▓▓▓   ▓▓▓          ┃
┃ ▓▓  ▓▓▓  ▓ ▓    ▓ ▓▓ ▓   ▓  ▓ ▓┃    ┃ ▓▓   ▓▓   ▓▓      ▓▓▓▓         ┃
┃▓ ▓ ▓  ▓▓ ▓▓   ▓  ▓  ▓▓▓▓  ▓ ▓▓ ┃    ┃      ▓▓  ▓▓▓      ▓▓▓▓      ▓▓ ┃
┃   ▓▓▓▓   ▓▓▓ ▓▓ ▓ ▓▓▓  ▓     ▓ ┃    ┃          ▓▓▓▓     ▓▓▓▓      ▓▓ ┃
┃▓   ▓   ▓▓▓ ▓▓    ▓▓▓▓ ▓ ▓ ▓ ▓▓ ┃    ┃         ▓▓▓▓▓     ▓▓▓          ┃
┃ ▓▓  ▓ ▓ ▓▓▓▓▓ ▓ ▓       ▓      ┃    ┃       ▓▓▓▓▓▓▓▓     ▓▓          ┃
┃▓    ▓▓ ▓ ▓▓ ▓▓   ▓ ▓▓ ▓▓ ▓▓▓ ▓▓┃    ┃      ▓▓▓▓▓▓▓▓▓     ▓▓    ▓▓▓▓▓▓┃
┃  ▓▓▓  ▓▓▓▓▓ ▓▓    ▓▓▓▓   ▓▓▓▓▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓     ▓▓    ▓▓▓▓▓▓┃
┃  ▓  ▓ ▓▓▓▓▓ ▓ ▓ ▓     ▓ ▓▓▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓▓┃
┃▓ ▓ ▓ ▓▓▓▓▓▓ ▓▓▓▓    ▓▓▓   ▓   ▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓            ░ ┃
┃▓   ▓▓▓▓ ▓  ▓▓▓ ▓▓ ▓   ▓  ▓   ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓              ┃
┃ ▓   ▓▓▓▓ ▓▓  ▓▓ ▓ ▓▓▓▓ ▓   ▓  ▓┃    ┃     ▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓         ┃
┃     ▓▓▓  ▓  ▓▓▓▓  ▓ ▓▓ ▓  ▓▓▓▓▓┃    ┃     ▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓     ▓▓  ┃
┃   ▓▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓  ▓    ▓  ▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ▓▓    ▓▓▓  ┃
┃  ▓▓▓ ▓▓▓▓▓ ▓▓▓ ▓    ▓▓▓   ▓▓ ▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓▓  ┃
┃ ▓    ▓▓  ▓ ▓▓▓▓ ▓     ▓ ▓ ▓▓▓  ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓       ▓   ▓▓▓  ┃
┃▓▓▓ ▓ ▓▓▓▓  ▓▓   ▓ ▓   ▓▓  ▓ ▓  ┃    ┃▓▓▓  ▓▓▓▓▓▓▓▓▓         ▓░░▓▓▓   ┃
┃▓▓▓ ▓▓▓ ▓▓▓▓▓  ▓   ▓  ▓▓ ▓ ▓   ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓░░▓▓▓   ┃
┃▓ ▓▓ ▓  ▓▓▓▓▓▓ ▓  ▓▓ ▓▓  ▓▓▓ ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓░░▓▓▓▓▓▓┃
┃ ▓▓  ▓ ▓▓▓▓▓ ▓▓▓▓   ▓▓▓▓  ▓ ▓▓▓▓┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ▓▓▓▓▓┃
┃▓▓▓▓ ▓ ▓▓▓   ▓▓▓▓ ▓▓    ▓  ▓ ▓▓ ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░    ▓▓▓ ┃
┃▓▓▓ ▓  ▓ ▓▓▓ ▓▓  ▓▓▓ ▓ ▓  ▓  ▓  ┃    ┃▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░    ▓▓  ┃
┃▓▓    ▓   ▓ ▓  ▓▓▓  ▓▓▓▓  ▓▓▓▓  ┃    ┃▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓  ┃
┃▓ ▓▓ ▓▓  ▓ ▓▓▓▓ ▓ ▓▓  ▓         ┃    ┃▓▓▓▓        ▓▓▓▓     ▓▓▓        ┃
┃▓  ▓▓    ▓  ▓▓ ▓     ▓▓▓▓ ▓    ▓┃    ┃  ▓▓        ▓▓       ▓▓▓▓       ┃
┃  ▓▓ ▓ ▓   ▓▓ ▓  ▓ ▓▓  ▓ ▓▓ ▓▓▓ ┃    ┃  ▓▓░       ▓▓       ▓▓▓▓▓▓     ┃
┃ ▓ ▓▓ ▓       ▓  ▓   ▓▓▓ ▓▓▓    ┃    ┃   ░                ▓▓▓▓▓▓▓     ┃
┃▓      ▓▓▓▓▓▓▓ ▓   ▓▓▓  ▓ ▓    ▓┃    ┃          ▓▓▓      ▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓     ▓ ▓ ▓▓ ▓▓▓▓  ▓ ▓ ▓   ▓┃    ┃          ▓▓▓    ▓▓▓▓▓▓▓▓       ┃
┃▓    ▓▓▓▓ ▓ ▓  ▓ ▓  ▓▓▓ ▓ ▓  ▓ ▓┃    ┃       ▓▓ ▓▓▓    ▓▓▓▓▓▓▓        ┃
┃▓  ▓   ▓▓ ▓▓ ▓▓ ▓▓ ▓ ▓ ▓  ▓▓  ▓ ┃    ┃       ▓▓                       ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓  ▓▓  ▓▓▓▓▓▓  ▓▓▓▓ ▓  ▓▓ ▓▓▓┃    ┃            ▓▓▓    ▓▓        ▓▓ ┃
┃▓▓  ▓▓▓ ▓▓ ▓ ▓  ▓   ▓     ▓  ▓▓ ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ▓▓        ▓▓ ┃
┃▓▓ ▓  ▓▓ ▓▓  ▓▓▓▓  ▓▓  ▓▓    ▓▓ ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ▓▓    ▓▓ ┃
┃    ▓▓  ▓▓▓▓▓    ▓ ▓▓  ▓▓ ▓▓   ▓┃    ┃        ▓▓▓▓       ▓▓  ▓▓       ┃
┃ ▓      ▓ ▓   ▓  ▓ ▓▓   ▓  ▓▓  ▓┃    ┃        ▓▓         ▓▓           ┃
┃▓▓  ▓▓▓▓▓   ▓▓▓▓       ▓    ▓▓ ▓┃    ┃▓▓  ▓▓▓▓▓▓                    ▓▓┃
┃▓  ▓▓▓ ▓▓ ▓▓ ▓    ▓▓▓▓▓  ▓▓ ▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓         ▓▓▓▓        ▓▓┃
┃▓▓▓▓▓▓▓▓▓▓     ▓ ▓▓ ▓  ▓▓▓    ▓▓┃    ┃▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓  ▓▓▓   ▓▓┃
┃ ▓  ▓▓ ▓▓  ▓▓ ▓▓▓▓▓ ▓▓   ▓▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓   ▓▓▓   ▓▓┃
┃▓ ▓▓▓     ▓ ▓ ▓▓▓▓ ▓▓   ▓▓ ▓  ▓▓┃    ┃  ▓▓▓▓▓░    ▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓┃
┃   ▓▓ ▓▓▓▓ ▓▓▓▓▓ ▓    ▓▓▓▓      ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓      ┃
┃   ▓  ▓ ▓      ▓ ▓   ▓▓▓▓ ▓     ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓      ┃
┃  ▓▓▓▓▓▓▓▓ ▓▓▓  ▓▓       ▓  ▓ ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓      ┃
┃  ▓▓ ▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓ ▓ ┃    ┃  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓   ┃
┃    ▓▓ ▓ ▓▓  ▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓ ▓ ▓┃    ┃   ░░░   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓▓      ▓▓  ▓▓▓▓ ▓   ▓ ▓  ▓ ▓ ┃    ┃   ░░░   ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓  ░░  ┃
┃▓   ▓ ▓▓ ▓ ▓▓▓        ▓▓▓▓  ▓ ▓ ┃    ┃   ░░░   ▓▓▓           ▓▓▓  ░░░ ┃
┃▓▓▓▓▓▓  ▓▓▓▓   ▓ ▓▓      ▓▓ ▓ ▓▓┃    ┃▓▓  ░▓▓▓▓▓▓▓    ▓▓     ▓▓▓▓▓░░  ┃
┃▓▓    ▓▓▓▓    ▓▓▓▓ ▓   ▓▓▓ ▓  ▓ ┃    ┃▓▓   ▓▓▓▓▓▓   ▓▓▓▓     ▓▓▓▓▓▓░  ┃
┃ ▓  ▓▓ ▓▓▓ ▓▓▓▓▓▓ ▓   ▓▓  ▓▓▓ ▓▓┃    ┃▓▓   ▓▓▓▓▓▓  ▓▓▓▓▓    ▓▓  ▓▓▓▓  ┃
┃▓▓ ▓ ▓▓▓▓▓▓   ▓▓ ▓▓▓▓▓▓▓  ▓▓ ▓  ┃    ┃▓▓░░▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓  ┃
┃ ▓▓  ▓▓▓  ▓  ▓ ▓▓    ▓▓▓▓    ▓ ▓┃    ┃   ░▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ┃
┃▓  ▓▓  ▓ ▓▓    ▓▓▓▓ ▓▓▓   ▓▓▓▓▓ ┃    ┃    ▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓  ┃
┃▓  ▓ ▓▓▓ ▓  ▓▓▓   ▓ ▓▓▓▓▓  ▓   ▓┃    ┃     ▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓  ▓▓▓ ▓     ▓ ▓▓▓    ▓▓▓▓▓▓▓ ┃    ┃     ▓▓▓▓             ▓▓▓▓▓▓▓▓  ┃
┃▓    ▓▓▓▓  ▓ ▓        ▓▓   ▓▓▓ ▓┃    ┃     ▓▓▓▓             ▓▓▓▓▓▓▓▓  ┃
┃▓       ▓ ▓  ▓ ▓  ▓▓▓ ▓▓▓ ▓   ▓▓┃    ┃                     ▓▓▓▓       ┃
┃  ▓      ▓ ▓ ▓ ▓▓▓  ▓  ▓▓▓     ▓┃    ┃                    ▓▓▓▓▓       ┃
┃  ▓   ▓▓     ▓  ▓   ▓▓▓▓   ▓▓▓  ┃    ┃      ▓▓            ▓▓▓▓   ▓▓   ┃
┃ ▓   ▓▓▓▓▓▓▓▓▓▓  ▓   ▓   ▓▓▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓░       ▓▓▓   ▓▓▓   ┃
┃ ▓▓▓▓▓  ▓▓ ▓  ▓▓    ▓▓▓   ▓    ▓┃    ┃    ▓▓▓▓▓▓▓               ▓▓▓   ┃
┃▓   ▓▓ ▓ ▓     ▓  ▓    ▓ ▓▓▓▓▓ ▓┃    ┃    ▓▓                    ▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓  ▓▓▓     ▓ ▓▓ ▓    ▓▓▓  ▓▓  ┃    ┃     ▓▓▓       ▓▓▓              ┃
┃▓ ▓  ▓▓▓▓ ▓▓   ▓▓▓▓ ▓      ▓▓   ┃    ┃     ▓▓▓▓      ▓▓▓▓         ▓▓  ┃
┃ ▓ ▓▓▓  ▓    ▓ ▓ ▓▓▓   ▓▓▓   ▓▓ ┃    ┃ ▓▓▓▓▓  ▓     ▓▓▓▓▓         ▓▓  ┃
┃ ▓ ▓ ▓  ▓ ▓▓▓ ▓▓▓       ▓ ▓ ▓▓ ▓┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓▓▓▓       ▓▓   ▓▓  ┃
┃ ▓▓  ▓▓▓▓▓ ▓ ▓▓     ▓▓▓▓▓   ▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓       ┃
┃  ▓▓  ▓  ▓▓ ▓▓ ▓ ▓  ▓  ▓       ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓       ┃
┃▓  ▓▓▓▓ ▓ ▓▓▓ ▓ ▓ ▓▓▓▓▓▓▓▓▓▓▓▓ ▓┃    ┃  ▓▓▓▓▓  ▓▓▓▓▓▓▓░▓▓▓▓▓▓▓▓       ┃
┃ ▓▓   ▓   ▓    ▓  ▓▓  ▓   ▓     ┃    ┃ ▓▓       ░▓▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃ ▓▓ ▓  ▓▓ ▓ ▓▓  ▓▓ ▓▓ ▓▓  ▓ ▓▓ ▓┃    ┃ ▓▓       ░░▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓ ┃
┃▓     ▓   ▓ ▓▓▓▓▓  ▓▓  ▓▓▓  ▓▓▓ ┃    ┃          ░░▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓ ┃
┃▓▓   ▓ ▓▓▓ ▓    ▓ ▓▓▓  ▓▓ ▓▓  ▓ ┃    ┃       ▓▓▓░░░    ▓▓▓▓  ▓▓▓▓▓▓   ┃
┃   ▓▓  ▓▓  ▓ ▓▓▓ ▓▓ ▓▓▓▓ ▓ ▓▓  ▓┃    ┃       ▓▓▓░░      ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃  ▓   ▓ ▓▓ ▓ ▓  ▓       ▓▓   ▓ ▓┃    ┃       ▓▓▓░            ▓▓▓      ┃
┃ ▓  ▓▓  ▓▓ ▓▓   ▓  ▓   ▓▓▓ ▓▓▓ ▓┃    ┃    ▓▓▓▓▓▓             ▓▓▓      ┃
┃    ▓▓▓▓▓    ▓   ▓  ▓ ▓       ▓ ┃    ┃    ▓▓▓▓▓▓                      ┃
┃  ▓▓   ▓▓▓ ▓  ▓▓ ▓ ▓  ▓▓  ▓▓   ▓┃    ┃  ▓▓▓  ▓▓▓                      ┃
┃ ▓▓▓▓  ▓▓ ▓▓▓▓   ▓   ▓▓  ▓ ▓ ▓▓▓┃    ┃ ▓▓▓▓  ▓▓▓           ▓▓   ▓▓    ┃
┃ ▓▓▓ ▓    ▓     ▓ ▓ ▓▓ ▓▓▓ ▓   ▓┃    ┃ ▓▓▓▓                ▓▓   ▓▓    ┃
┃▓▓ ▓     ▓ ▓▓   ▓▓ ▓      ▓    ▓┃    ┃ ▓▓▓▓           ▓▓░░░░         ░┃
┃  ▓▓▓▓▓ ▓▓    ▓  ▓▓ ▓▓▓  ▓ ▓▓ ▓▓┃    ┃  ▓▓▓           ▓▓░░░░        ▓▓┃
┃▓ ▓  ▓    ▓   ▓ ▓▓   ▓ ▓▓▓   ▓▓▓┃    ┃                ▓▓  ▓▓  ▓▓    ▓▓┃
┃▓   ▓  ▓▓▓ ▓▓ ▓ ▓  ▓▓▓  ▓▓    ▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓     ▓▓  ▓▓      ┃
┃   ▓▓▓▓▓ ▓▓▓ ▓▓▓     ▓▓  ▓▓▓▓ ▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓     ▓▓   ▓▓▓▓   ┃
┃ ▓▓ ▓▓▓  ▓▓  ▓    ▓ ▓ ▓    ▓▓ ▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓            ▓▓   ┃
┃  ▓▓▓▓ ▓  ▓▓▓ ▓▓▓ ▓▓ ▓ ▓    ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓   ┃
┃  ▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓▓  ▓▓  ▓▓▓▓ ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓   ┃
┃     ▓▓▓▓▓ ▓▓▓   ▓ ▓▓     ▓▓▓  ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓     ▓▓▓▓▓ ┃
┃  ▓▓▓  ▓▓▓▓ ▓▓▓    ▓▓ ▓    ▓▓▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓     ▓▓     ▓▓▓▓▓▓┃
┃▓    ▓  ▓  ▓▓         ▓▓▓ ▓▓ ▓ ▓┃    ┃     ▓▓▓▓▓  ▓▓        ▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓ ▓▓ ▓   ▓▓▓      ▓▓▓ ▓▓ ▓▓▓┃    ┃      ▓▓▓   ▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓┃
┃   ▓ ▓ ▓▓ ▓ ▓▓ ▓ ▓▓ ▓▓▓▓ ▓  ▓▓  ┃    ┃      ▓▓     ▓▓▓  ▓▓▓▓▓▓▓       ┃
┃   ▓ ▓▓▓     ▓ ▓  ▓▓▓▓ ▓ ▓ ▓ ▓  ┃    ┃      ▓▓          ▓▓▓▓▓         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓       ▓ ▓ ▓  ▓▓ ▓▓ ▓   ▓ ▓▓┃    ┃                  ▓▓▓▓▓▓        ┃
┃▓ ▓  ▓ ▓▓▓  ▓   ▓ ▓▓▓ ▓▓▓  ▓▓  ▓┃    ┃                  ▓▓▓▓▓▓▓       ┃
┃▓             ▓▓▓ ▓▓ ▓▓▓▓   ▓▓▓ ┃    ┃               ▓▓▓▓▓▓▓▓▓▓  ▓▓▓  ┃
┃▓▓▓    ▓ ▓▓▓  ▓ ▓▓   ▓ ▓  ▓▓▓   ┃    ┃         ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓▓▓▓ ▓ ▓▓▓ ▓▓ ▓▓▓▓▓▓ ▓▓  ▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓  ▓  ▓▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓ ▓  ▓▓▓ ▓▓▓▓▓ ▓▓  ▓▓▓▓▓▓▓▓▓   ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓ ▓ ▓ ▓▓  ▓▓▓ ▓▓▓ ▓▓▓   ▓▓▓▓▓▓▓┃    ┃   ▓▓▓▓▓▓  ▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓  ┃
┃ ▓▓▓▓▓ ▓   ▓        ▓▓ ▓   ▓    ┃    ┃   ▓▓▓▓▓▓          ▓▓▓   ▓▓▓▓   ┃
┃    ▓▓▓▓▓    ▓▓ ▓▓▓▓    ▓▓▓ ▓▓ ▓┃    ┃    ▓▓▓▓▓    ▓▓  ▓▓▓▓  ▓▓▓▓     ┃
┃ ▓   ▓▓▓▓▓▓▓ ▓▓  ▓ ▓▓ ▓▓▓▓  ▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓ ▓▓▓▓      ┃
┃▓▓▓▓ ▓   ▓▓▓▓    ▓▓▓▓ ▓▓   ▓  ▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓ ▓▓        ┃
┃ ▓ ▓▓ ▓▓▓ ▓▓▓▓▓ ▓ ▓▓   ▓  ▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓      ▓▓┃
┃  ▓  ▓ ▓▓▓   ▓▓▓ ▓ ▓   ▓▓▓  ▓ ▓▓┃    ┃       ▓▓▓   ▓▓▓▓▓▓▓   ▓▓▓    ▓▓┃
┃▓▓   ▓    ▓   ▓▓ ▓ ▓  ▓ ▓▓ ▓  ▓ ┃    ┃             ▓▓▓▓▓▓▓   ▓▓▓▓░░   ┃
┃▓    ▓   ▓  ▓ ▓ ▓  ▓ ▓  ▓ ▓ ▓▓▓ ┃    ┃▓▓           ▓▓▓▓  ▓▓▓▓▓▓▓▓░    ┃
┃▓▓ ▓▓ ▓ ▓    ▓▓  ▓ ▓▓ ▓ ▓▓ ▓ ▓  ┃    ┃▓▓▓▓▓        ▓▓▓   ▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓▓ ▓ ▓▓▓▓▓ ▓▓  ▓▓▓▓   ▓▓▓   ▓┃    ┃▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓     ┃
┃▓  ▓▓  ▓ ▓▓▓▓  ▓    ▓ ▓▓▓       ┃    ┃  ▓▓▓  ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓     ┃
┃ ▓ ▓▓  ▓▓   ▓▓▓    ▓▓▓▓▓▓▓▓     ┃    ┃   ▓▓  ▓▓  ▓▓▓▓▓   ▓▓▓▓▓▓▓▓     ┃
┃ ▓  ▓ ▓▓▓  ▓  ▓▓ ▓▓▓▓  ▓ ▓▓▓ ▓  ┃    ┃       ▓▓  ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓    ┃
┃    ▓    ▓▓▓▓▓▓  ▓▓ ▓    ▓ ▓▓ ▓ ┃    ┃          ▓▓▓▓▓▓▓▓▓▓      ▓▓    ┃
┃ ▓▓  ▓ ▓  ▓▓ ▓▓▓▓▓▓   ▓▓  ▓  ▓▓▓┃    ┃ ▓▓       ▓▓▓▓▓▓▓▓▓       ░░    ┃
┃▓▓▓  ▓▓   ▓ ▓▓▓ ▓ ▓ ▓▓  ▓  ▓    ┃    ┃ ▓▓       ▓▓▓▓▓▓▓▓        ░░    ┃
┃   ▓ ▓ ▓  ▓▓▓▓ ▓    ▓    ▓▓ ▓   ┃    ┃          ▓▓▓▓▓▓▓▓        ░░    ┃
┃  ▓▓ ▓▓    ▓▓  ▓▓▓▓  ▓▓▓▓  ▓    ┃    ┃  ▓▓▓▓     ▓▓▓▓▓▓▓      ▓▓▓▓    ┃
┃ ▓ ▓▓  ▓ ▓ ▓▓▓ ▓ ▓ ▓   ▓ ▓▓   ▓ ┃    ┃  ▓▓▓▓░    ▓▓▓▓▓▓      ▓▓▓▓▓    ┃
┃▓▓▓ ▓▓  ▓▓ ▓ ▓▓▓▓ ▓▓▓ ▓ ▓▓▓▓    ┃    ┃▓▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓    ┃
┃▓▓▓  ▓ ▓▓ ▓    ▓▓▓ ▓   ▓ ▓ ▓▓ ▓ ┃    ┃▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓   ┃
┃   ▓▓▓  ▓▓▓ ▓ ▓▓  ▓  ▓ ▓▓▓▓ ▓ ▓ ┃    ┃    ▓▓  ▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓  ┃
┃     ▓ ▓ ▓ ▓ ▓▓   ▓ ▓▓▓ ▓ ▓▓▓▓ ▓┃    ┃        ▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓  ┃
┃▓▓   ▓ ▓ ▓▓▓▓▓  ▓ ▓   ▓▓     ▓▓ ┃    ┃         ▓▓▓▓▓                  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓▓ ▓ ▓▓ ▓▓  ▓   ▓  ▓ ▓     ▓  ┃    ┃                                ┃
┃ ▓▓   ▓     ▓▓▓  ▓▓  ▓▓ ▓ ▓  ▓  ┃    ┃                                ┃
┃   ▓ ▓          ▓   ▓  ▓▓▓▓  ▓▓ ┃    ┃                     ▓▓▓▓▓      ┃
┃   ▓▓▓ ▓     ▓  ▓▓   ▓▓▓▓ ▓ ▓ ▓ ┃    ┃    ▓▓▓         ▓▓  ▓▓▓▓▓▓      ┃
┃ ▓ ▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓  ▓▓ ▓ ▓   ▓  ┃    ┃    ▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓▓▓▓      ┃
┃▓▓  ▓ ▓▓▓▓  ▓▓ ▓▓▓ ▓▓ ▓▓▓▓   ▓▓▓┃    ┃▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓    ▓▓▓┃
┃▓▓▓ ▓▓▓  ▓▓▓ ▓▓▓   ▓ ▓▓    ▓▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓   ▓▓▓▓┃
┃▓▓▓▓  ▓ ▓ ▓▓▓▓▓ ▓  ▓▓ ▓▓ ▓▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓ ▓ ▓  ▓ ▓▓  ▓  ▓▓  ▓▓▓▓▓▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓▓▓ ▓  ▓ ▓▓ ▓▓▓▓   ▓  ▓ ▓▓▓  ┃    ┃ ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓  ┃
┃  ▓   ▓  ▓▓▓  ▓ ▓▓▓   ▓▓▓ ▓ ▓   ┃    ┃         ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓  ┃
┃▓▓   ▓   ▓▓ ▓▓ ▓▓▓▓ ▓ ▓▓▓▓▓▓▓▓▓ ┃    ┃         ▓▓▓▓▓▓░▓▓▓▓  ▓▓▓▓▓▓▓▓  ┃
┃ ▓   ▓ ▓▓▓▓ ▓   ▓▓ ▓▓ ▓▓▓▓▓▓    ┃    ┃         ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓▓        ▓ ▓    ▓▓ ▓      ▓   ┃    ┃ ▓▓             ▓▓▓▓▓▓          ┃
┃  ▓▓▓▓▓▓▓▓    ▓ ▓▓▓▓▓    ▓   ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓           ┃
┃▓▓  ▓▓ ▓▓▓ ▓▓  ▓ ▓   ▓ ▓▓▓▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓      ▓▓▓             ┃
┃▓ ▓▓▓▓▓  ▓       ▓ ▓         ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓      ▓▓▓             ┃
┃ ▓▓  ▓▓ ▓▓    ▓▓▓▓▓▓▓  ▓▓  ▓  ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓      ▓▓▓          ░  ┃
┃▓ ▓▓▓   ▓        ▓ ▓ ▓ ▓ ▓ ▓ ▓  ┃    ┃▓▓▓▓▓           ▓▓▓▓▓▓▓▓▓     ░ ┃
┃▓▓▓ ▓  ▓    ▓ ▓▓ ▓  ▓▓▓▓▓▓  ▓▓▓▓┃    ┃▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓       ┃
┃▓▓  ▓ ▓▓▓▓ ▓ ▓▓▓▓  ▓▓▓▓ ▓  ▓  ▓ ┃    ┃▓▓  ▓▓▓▓▓▓    ▓▓   ▓▓▓▓▓▓▓      ┃
┃▓   ▓ ▓▓ ▓ ▓  ▓▓ ▓ ▓ ▓▓  ▓▓▓ ▓ ▓┃    ┃▓▓  ▓▓▓▓▓▓▓   ▓▓    ▓▓▓▓▓▓▓     ┃
┃▓▓▓▓ ▓▓▓▓▓▓  ▓  ▓    ▓▓ ▓ ▓     ┃    ┃▓▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓▓     ┃
┃  ▓▓▓▓▓▓▓ ▓     ▓     ▓ ▓▓▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓           ▓▓▓▓▓     ┃
┃   ▓▓▓ ▓▓ ▓▓▓   ▓▓    ▓▓▓ ▓▓ ▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓▓    ┃
┃   ▓▓   ▓▓ ▓   ▓    ▓ ▓▓ ▓▓     ┃    ┃   ▓▓▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓    ┃
┃ ▓   ▓ ▓▓▓▓▓▓  ▓ ▓▓ ▓     ▓▓    ┃    ┃   ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓      ▓▓    ┃
┃▓▓▓ ▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓▓   ▓▓ ▓  ▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓    ┃
┃▓▓▓▓▓ ▓ ▓▓    ▓  ▓▓▓   ▓  ▓▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓  ┃
┃  ▓▓▓  ▓▓▓▓▓▓▓  ▓▓  ▓ ▓   ▓▓▓ ▓ ┃    ┃  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓  ┃
┃   ▓    ▓   ▓▓▓▓ ▓▓▓   ▓ ▓▓  ▓▓▓┃    ┃            ▓▓▓▓▓▓▓▓            ┃
┃▓    ▓▓   ▓ ▓  ▓   ▓   ▓▓ ▓ ▓   ┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓ ▓    ▓  ▓ ▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓▓┃    ┃                        ▓▓▓▓    ┃
┃▓ ▓▓ ▓▓▓▓▓  ▓▓▓ ▓ ▓▓▓▓  ▓▓  ▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓    ┃
┃▓▓▓▓  ▓▓▓    ▓  ▓    ▓▓▓▓ ▓ ▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓     ┃
┃  ▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓▓▓ ▓▓▓▓▓▓▓▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓     ░▓▓▓▓▓▓▓▓▓▓      ┃
┃▓  ▓   ▓▓▓   ▓ ▓ ▓▓▓▓▓▓▓▓    ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓    ░░▓▓▓▓▓▓▓▓▓       ┃
┃▓▓▓▓▓ ▓    ▓▓  ▓ ▓  ▓▓▓      ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓          ▓▓▓▓▓        ┃
┃▓ ▓▓ ▓▓▓▓▓  ▓   ▓  ▓▓ ▓▓  ▓▓▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓          ▓▓▓▓▓  ▓▓▓▓  ┃
┃ ▓ ▓ ▓▓▓▓ ▓ ▓     ▓ ▓▓▓▓▓▓▓▓▓▓▓ ┃    ┃   ▓▓▓▓▓▓          ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃    ▓▓  ▓   ▓     ▓      ▓  ▓   ┃    ┃   ▓▓▓▓▓▓▓                      ┃
┃▓▓▓ ▓▓▓ ▓ ▓  ▓ ▓▓ ▓ ▓   ▓  ▓  ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓                      ┃
┃▓▓▓▓ ▓▓ ▓▓▓ ▓▓     ▓▓▓▓ ▓ ▓▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓     ▓▓    ┃
┃▓▓   ▓▓▓▓▓▓ ▓   ▓ ▓  ▓  ▓ ▓▓ ▓▓▓┃    ┃▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓▓     ▓▓░░▓▓┃
┃  ▓▓    ▓▓▓  ▓ ▓▓ ▓▓▓   ▓ ▓ ▓ ▓ ┃    ┃ ░░   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ░░░░▓▓┃
┃ ▓    ▓▓▓▓▓▓▓▓▓ ▓▓▓  ▓ ▓ ▓ ▓▓ ▓▓┃    ┃ ░░   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ░   ░░░░▓▓┃
┃▓▓▓ ▓ ▓▓  ▓   ▓  ▓▓▓ ▓▓     ▓ ▓▓┃    ┃ ▓▓   ▓▓     ▓▓▓▓▓▓▓  ░░      ▓▓┃
┃ ▓▓▓   ▓  ▓  ▓▓▓▓ ▓ ▓  ▓ ▓▓   ▓▓┃    ┃ ▓▓   ▓▓     ▓▓▓▓     ░░      ▓▓┃
┃  ▓ ▓▓ ▓▓ ▓ ▓▓ ▓   ▓  ▓  ▓   ▓▓▓┃    ┃      ▓▓    ▓▓▓▓      ▓▓▓▓   ▓▓▓┃
┃▓    ▓▓     ▓▓▓ ▓  ▓  ▓▓▓▓   ▓  ┃    ┃     ░░░    ▓▓▓       ▓▓▓▓   ▓▓▓┃
┃ ▓▓  ▓ ▓   ▓    ▓▓▓▓▓ ▓▓ ▓▓  ▓▓▓┃    ┃     ░░░            ▓▓▓▓▓▓▓  ▓▓▓┃
┃      ▓▓ ▓ ▓▓   ▓ ▓  ▓▓   ▓▓   ▓┃    ┃     ▓▓▓            ▓▓▓  ▓▓     ┃
┃▓  ▓ ▓▓▓  ▓  ▓ ▓    ▓▓▓  ▓▓ ▓  ▓┃    ┃    ▓▓▓▓▓           ▓▓▓  ▓▓▓    ┃
┃▓ ▓ ▓▓▓ ▓▓▓▓ ▓     ▓▓ ▓   ▓▓▓   ┃    ┃   ▓▓▓▓▓▓           ▓▓▓  ▓▓▓▓   ┃
┃▓  ▓▓   ▓    ▓▓  ▓ ▓  ▓▓ ▓▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓    ▓▓     ▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓▓ ▓▓▓▓  ▓▓ ▓▓▓   ▓▓▓▓▓  ▓   ▓┃    ┃  ▓▓▓▓▓▓▓    ▓▓▓    ▓▓▓▓▓▓▓▓▓   ┃
┃  ▓▓▓▓ ▓▓▓    ▓▓    ▓    ▓▓▓ ▓ ▓┃    ┃  ▓▓▓▓▓▓▓     ▓▓    ▓    ▓▓▓▓   ┃
┃▓   ▓▓  ▓  ▓ ▓   ▓ ▓▓    ▓ ▓▓ ▓▓┃    ┃  ▓▓▓▓  ▓▓        ▓▓▓    ▓▓▓▓   ┃
┃▓▓▓▓ ▓▓ ▓▓▓   ▓  ▓▓▓ ▓   ▓▓ ▓▓ ▓┃    ┃  ▓▓▓▓  ▓▓        ▓▓▓    ▓▓▓▓   ┃
┃ ▓  ▓       ▓ ▓▓  ▓       ▓     ┃    ┃    ▓▓        ▓▓   ░░           ┃
┃    ▓▓▓  ▓▓ ▓  ▓▓  ▓ ▓    ▓  ▓▓▓┃    ┃    ▓▓       ▓▓▓   ░░         ▓▓┃
┃▓▓ ▓▓▓ ▓  ▓ ▓ ▓▓ ▓ ▓▓  ▓    ▓ ▓▓┃    ┃    ▓▓      ▓▓▓▓   ▓▓▓        ▓▓┃
┃▓    ▓  ▓   ▓▓ ▓   ▓▓▓▓▓▓  ▓▓   ┃    ┃            ▓▓▓▓   ▓▓▓▓▓        ┃
┃ ▓  ▓ ▓▓▓  ▓▓▓ ▓▓▓ ▓ ▓▓ ▓ ▓▓  ▓▓┃    ┃            ▓▓▓▓    ▓▓▓▓        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓  ▓    ▓ ▓ ▓ ▓▓▓▓   ▓ ▓  ▓┃    ┃    ▓▓             ▓▓▓          ┃
┃▓   ▓▓▓▓ ▓     ▓▓ ▓▓▓ ▓ ▓▓▓▓▓▓  ┃    ┃    ▓▓▓▓          ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓▓ ▓ ▓ ▓▓ ▓▓    ▓▓ ▓▓ ▓▓  ▓▓┃    ┃ ▓▓▓▓▓▓▓░        ▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃ ▓▓ ▓   ▓ ▓ ▓  ▓ ▓▓▓   ▓    ▓  ▓┃    ┃ ▓▓▓▓▓▓▓░░ ▓▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃ ▓▓▓▓ ▓▓▓    ▓▓▓▓▓▓▓ ▓▓▓ ▓     ▓┃    ┃ ▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃   ▓ ▓    ▓▓▓▓  ▓  ▓▓ ▓  ▓▓ ▓   ┃    ┃ ▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓▓        ▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓  ▓ ┃    ┃ ▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃ ▓▓ ▓▓▓▓▓▓▓▓▓  ▓▓▓ ▓▓▓  ▓▓    ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓▓  ▓ ▓ ▓  ▓▓ ▓▓    ▓ ▓   ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ░░░░  ▓▓▓▓┃
┃   ▓▓▓▓▓   ▓▓ ▓   ▓▓   ▓ ▓▓ ▓ ▓▓┃    ┃  ▓▓▓▓▓   ▓▓▓     ▓▓  ░░░   ▓▓▓▓┃
┃ ▓ ▓      ▓▓▓   ▓ ▓▓▓▓▓ ▓ ▓ ▓▓ ▓┃    ┃  ▓▓      ▓▓▓     ▓▓▓▓▓░    ▓▓▓ ┃
┃▓▓▓▓   ▓▓▓ ▓ ▓  ▓ ▓▓▓▓▓   ▓  ▓▓ ┃    ┃ ▓▓▓   ▓▓▓▓▓▓    ▓▓▓▓▓▓      ▓▓ ┃
┃▓ ▓  ▓▓▓ ▓  ▓  ▓▓ ▓▓ ▓ ▓   ▓ ▓▓ ┃    ┃ ▓▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓       ▓▓ ┃
┃ ▓▓ ▓▓▓▓ ▓▓▓▓▓▓ ▓▓▓▓▓  ▓▓    ▓ ▓┃    ┃ ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓           ┃
┃ ▓  ▓ ▓   ▓▓▓▓▓  ▓▓▓  ▓▓ ▓ ▓   ▓┃    ┃ ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓           ┃
┃ ▓▓      ▓▓ ▓▓▓▓▓ ▓▓▓▓         ▓┃    ┃ ▓▓       ▓▓▓▓▓▓▓▓▓▓▓           ┃
┃▓ ▓▓▓ ▓▓   ▓▓▓▓ ▓▓▓▓    ▓▓▓▓  ▓▓┃    ┃ ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓      ▓▓    ┃
┃    ▓▓▓  ▓   ▓ ▓▓ ▓▓ ▓ ▓   ▓  ▓ ┃    ┃   ▓▓▓▓      ▓▓▓▓▓▓▓    ▓▓▓▓    ┃
┃▓  ▓▓▓ ▓ ▓ ▓  ▓ ▓▓▓  ▓▓▓▓▓▓▓ ▓  ┃    ┃   ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃ ▓▓▓▓▓▓ ▓▓▓  ▓▓ ▓  ▓▓     ▓ ▓   ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓   ▓▓    ┃
┃   ▓▓  ▓▓ ▓▓ ▓     ▓▓▓ ▓  ▓ ▓   ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓         ┃
┃ ▓   ▓▓  ▓ ▓▓▓▓▓    ▓▓▓ ▓   ▓ ▓ ┃    ┃   ▓▓▓▓   ▓▓▓▓▓     ▓▓▓         ┃
┃ ▓▓ ▓▓▓   ▓▓      ▓   ▓    ▓    ┃    ┃   ▓▓▓▓   ▓▓▓▓▓                 ┃
┃   ▓▓  ▓  ▓ ▓▓▓▓▓      ▓▓▓  ▓ ▓ ┃    ┃   ▓▓▓▓   ▓▓▓▓▓▓        ▓▓      ┃
┃ ▓ ▓ ▓▓▓ ▓▓▓▓▓▓▓  ▓ ▓    ▓ ▓ ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓    ┃
┃  ▓  ▓▓▓▓    ▓ ▓▓ ▓  ▓ ▓▓▓ ▓  ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓    ┃
┃   ▓     ▓ ▓▓ ▓▓▓  ▓  ▓  ▓ ▓   ▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓    ┃
┃▓ ▓▓  ▓▓▓ ▓▓▓  ▓▓▓ ▓▓ ▓▓ ▓▓▓    ┃    ┃       ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓ ▓▓ ▓▓ ▓ ▓  ▓▓ ▓▓▓▓▓▓▓   ▓▓▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓      ┃
┃   ▓▓▓▓ ▓▓ ▓ ▓▓▓  ▓  ▓  ▓▓  ▓   ┃    ┃   ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓      ┃
┃▓▓ ▓   ▓▓ ▓      ▓ ▓▓▓▓▓ ▓▓▓  ▓ ┃    ┃      ▓▓▓▓▓       ▓▓▓▓▓▓▓▓      ┃
┃ ▓  ▓▓▓ ▓▓ ▓▓▓ ▓ ▓▓▓ ▓▓    ▓▓  ▓┃    ┃       ▓▓▓        ▓▓▓▓▓         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓  ▓▓▓▓▓▓▓▓▓▓▓  ▓  ▓ ▓▓▓▓ ▓▓   ┃    ┃      ▓▓▓▓▓▓▓▓           ▓▓▓    ┃
┃ ▓ ▓   ▓▓  ▓ ▓  ▓  ▓▓     ▓▓  ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓▓    ┃
┃  ▓▓▓▓ ▓▓ ▓▓▓▓▓▓▓▓ ▓▓▓▓▓ ▓▓    ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓    ┃
┃ ▓▓▓▓▓▓▓   ▓ ▓ ▓▓ ▓▓  ▓  ▓▓▓▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓┃
┃   ▓▓ ▓  ▓▓ ▓▓▓▓▓▓▓▓    ▓ ▓▓▓▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓┃
┃ ▓▓  ▓▓▓ ▓   ▓  ▓▓▓   ▓     ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓     ┃
┃  ▓▓▓▓▓ ▓ ▓ ▓▓ ▓▓▓▓    ▓▓▓▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓┃
┃ ▓ ▓▓ ▓ ▓▓ ▓▓  ▓▓▓▓▓▓ ▓▓▓▓▓  ▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓┃
┃▓    ▓▓▓ ▓▓▓   ▓ ▓▓▓ ▓▓▓      ▓ ┃    ┃     ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓       ┃
┃  ▓  ▓ ▓        ▓▓   ▓ ▓▓   ▓ ▓ ┃    ┃     ▓▓        ░░░    ▓▓▓       ┃
┃▓▓▓▓▓ ▓   ▓    ▓ ▓      ▓  ▓▓   ┃    ┃  ▓▓▓▓▓        ░░░     ░░       ┃
┃▓  ▓▓▓▓   ▓ ▓  ▓▓      ▓  ▓ ▓▓ ▓┃    ┃  ▓▓▓▓▓        ▓▓▓     ░░  ▓▓▓  ┃
┃ ▓ ▓▓ ▓ ▓  ▓▓ ▓ ▓▓      ▓▓▓▓▓▓ ▓┃    ┃   ▓▓▓▓▓       ▓▓▓     ▓▓▓▓▓▓▓  ┃
┃  ▓   ▓▓  ▓ ▓   ▓ ▓▓▓▓ ▓▓▓ ▓▓▓ ▓┃    ┃      ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃    ▓  ▓▓▓ ▓  ▓▓▓▓▓  ▓▓ ▓▓    ▓ ┃    ┃      ▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓  ▓▓▓  ▓▓▓▓ ▓   ▓ ▓ ▓   ▓  ▓▓▓┃    ┃    ▓▓▓  ▓▓░░▓▓▓▓    ▓▓▓▓▓      ┃
┃▓ ▓▓ ▓   ▓▓  ▓▓ ▓▓  ▓ ▓▓▓▓    ▓ ┃    ┃▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓    ▓▓▓▓▓      ┃
┃▓▓▓ ▓▓▓      ▓▓▓▓  ▓ ▓▓▓  ▓ ▓ ▓ ┃    ┃▓▓▓▓▓▓▓      ▓▓▓▓    ▓▓▓▓▓      ┃
┃ ▓▓▓▓▓  ▓▓▓   ▓▓▓    ▓▓▓ ▓▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓  ▓▓   ▓▓▓    ▓▓▓▓▓▓  ▓▓ ┃
┃▓ ▓▓  ▓▓ ▓▓    ▓▓▓  ▓▓  ▓▓▓  ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓▓  ▓▓▓▓▓    ▓▓▓▓  ▓▓ ▓ ▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓  ▓▓▓▓▓  ▓▓  ▓ ▓    ▓▓ ▓▓▓▓▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓    ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓▓ ▓ ▓▓▓  ▓▓▓▓     ▓▓ ▓ ▓  ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓  ┃
┃▓  ▓ ▓▓   ▓▓▓▓▓ ▓ ▓    ▓▓▓ ▓▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓ ┃
┃▓▓  ▓ ▓ ▓▓ ▓▓▓▓▓ ▓▓  ▓  ▓ ▓ ▓▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓┃
┃ ▓ ▓  ▓▓▓▓▓▓ ▓ ▓ ▓   ▓ ▓▓▓  ▓ ▓▓┃    ┃      ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓       ▓    ▓▓     ▓▓▓▓ ▓▓ ▓▓ ▓┃    ┃             ▓▓      ▓▓▓▓▓      ┃
┃   ▓  ▓  ▓    ▓  ▓▓▓            ┃    ┃                                ┃
┃▓ ▓▓ ▓       ▓  ▓ ▓  ▓ ▓▓▓▓ ▓  ▓┃    ┃ ▓▓▓▓▓                   ▓▓     ┃
┃ ▓▓▓▓ ▓▓▓ ▓        ▓▓▓   ▓▓   ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓        ▓▓▓    ▓▓     ┃
┃ ▓  ▓ ▓ ▓▓▓▓  ▓▓  ▓▓     ▓ ▓  ▓ ┃    ┃       ▓▓▓▓▓  ▓▓  ▓▓▓    ▓▓     ┃
┃    ▓     ▓▓ ▓▓▓  ▓▓▓▓ ▓ ▓  ▓▓▓ ┃    ┃          ▓▓  ▓▓  ▓▓▓           ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓ ▓▓▓ ▓▓▓▓ ▓  ▓▓ ▓▓    ▓▓ ▓ ▓┃    ┃     ▓▓▓▓▓▓▓▓                   ┃
┃▓ ▓▓▓ ▓▓▓  ▓▓  ▓▓ ▓  ▓  ▓▓  ▓ ▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓   ┃
┃ ▓ ▓▓▓   ▓▓▓ ▓▓▓▓▓▓     ▓▓ ▓ ▓ ▓┃    ┃  ▓▓▓    ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓  ┃
┃ ▓▓▓▓    ▓ ▓▓ ▓  ▓▓▓▓▓ ▓ ▓▓▓ ▓ ▓┃    ┃  ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓  ┃
┃ ▓ ▓▓  ▓▓▓▓ ▓▓▓▓▓▓  ▓▓▓  ▓ ▓▓▓▓ ┃    ┃  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓  ┃
┃   ▓▓▓ ▓ ▓▓   ▓▓   ▓ ▓   ▓▓▓▓   ┃    ┃  ▓▓▓░░░▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓▓  ┃
┃ ▓▓▓▓ ▓ ▓▓  ▓▓ ▓▓    ▓▓▓▓▓  ▓▓▓▓┃    ┃   ▓▓░░░▓▓  ▓▓▓▓▓    ▓▓▓▓▓  ▓▓▓▓┃
┃▓  ▓ ▓▓  ▓  ▓▓ ▓   ▓ ▓▓▓    ▓  ▓┃    ┃   ░░░░░▓▓  ▓▓▓▓▓    ▓▓▓      ▓▓┃
┃▓   ▓   ▓▓ ▓   ▓▓ ▓   ▓▓  ▓   ▓▓┃    ┃   ░░░        ▓▓▓     ▓▓      ▓▓┃
┃  ▓▓ ▓    ▓▓ ▓▓▓   ▓  ▓  ▓▓   ▓▓┃    ┃   ▓▓▓        ▓▓▓        ▓▓   ▓▓┃
┃ ▓ ▓▓▓ ▓▓  ▓ ▓ ▓▓▓  ▓    ▓▓▓ ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓    ▓▓▓        ▓▓▓▓▓▓▓┃
┃▓▓ ▓ ▓▓ ▓ ▓   ▓   ▓  ▓▓  ▓▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓           ▓▓  ▓▓▓▓▓▓ ┃
┃▓ ▓  ▓▓▓▓▓  ▓      ▓ ▓▓▓    ▓▓▓▓┃    ┃▓▓   ▓▓▓▓▓          ▓▓▓▓    ▓▓▓ ┃
┃▓   ▓ ▓  ▓ ▓▓ ▓▓▓▓ ▓▓ ▓▓    ▓▓  ┃    ┃     ▓▓        ▓▓  ▓▓▓▓▓    ▓▓▓ ┃
┃ ▓▓ ▓ ▓   ▓     ▓   ▓ ▓▓▓▓ ▓  ▓ ┃    ┃      ▓  ░     ▓▓▓▓▓▓▓▓▓        ┃
┃ ▓ ▓  ▓▓▓▓▓▓▓  ▓▓▓▓▓▓  ▓      ▓ ┃    ┃ ▓▓   ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓          ┃
┃ ▓ ▓ ▓▓▓▓ ▓▓▓ ▓▓ ▓  ▓▓   ▓▓ ▓▓▓▓┃    ┃ ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓▓▓┃
┃▓▓▓ ▓  ▓▓▓▓ ▓ ▓▓ ▓  ▓▓▓   ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓▓▓┃
┃▓   ▓ ▓ ▓ ▓ ▓▓▓▓▓▓▓▓▓  ▓ ▓ ▓ ▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓┃
┃   ▓▓▓▓ ▓▓▓ ▓▓▓ ▓▓ ▓▓ ▓▓▓ ▓    ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓       ┃
┃▓ ▓▓▓▓ ▓ ▓▓▓▓▓ ▓   ▓▓   ▓▓    ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓       ┃
┃▓▓    ▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓ ▓▓    ▓  ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓ ▓▓  ▓▓▓▓▓▓ ▓  ▓ ▓ ▓▓▓  ▓   ▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓         ┃
┃   ▓▓▓▓ ▓ ▓▓▓ ▓ ▓ ▓   ▓  ▓ ▓  ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓       ▓         ┃
┃▓     ▓▓▓  ▓ ▓ ▓▓  ▓▓ ▓     ▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓       ▓         ┃
┃▓ ▓▓▓  ▓▓▓ ▓ ▓    ▓ ▓ ▓  ▓  ▓  ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓░       ▓         ┃
┃  ▓▓▓▓▓▓▓▓▓  ▓ ▓ ▓▓   ▓▓▓    ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓        ┃
┃   ▓▓▓▓ ▓▓ ▓▓▓▓  ▓   ▓▓ ▓ ▓  ▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓        ┃
┃▓      ▓▓ ▓▓▓ ▓  ▓▓ ▓      ▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓  ▓▓             ┃
┃▓▓  ▓▓ ▓   ▓ ▓▓ ▓▓▓  ▓ ▓▓▓▓▓▓  ▓┃    ┃           ▓▓▓▓  ▓▓    ▓▓▓▓▓    ┃
┃ ▓   ▓ ▓ ▓ ▓  ▓  ▓ ▓   ▓  ▓▓  ▓ ┃    ┃              ▓▓▓▓▓    ▓▓▓▓▓    ┃
┃ ▓   ▓  ▓    ▓▓▓▓▓    ▓▓ ▓▓▓ ▓▓▓┃    ┃              ▓▓▓▓        ▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓▓▓▓   ▓▓▓  ▓▓▓  ▓▓ ▓▓▓  ▓ ▓ ┃    ┃  ▓▓▓▓    ▓▓▓       ▓▓          ┃
┃  ▓▓▓▓  ▓▓▓ ▓▓▓  ▓▓▓▓▓     ▓▓   ┃    ┃  ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓          ┃
┃ ▓▓▓ ▓  ▓▓▓ ▓▓▓▓ ▓▓ ▓▓▓▓▓▓▓ ▓▓  ┃    ┃  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃         ▓▓▓ ▓▓▓  ▓   ▓ ▓ ▓▓▓ ▓ ┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓   ┃
┃ ▓▓   ▓▓▓  ▓▓▓   ▓▓▓  ▓ ▓      ▓┃    ┃ ▓▓        ▓▓▓▓   ▓▓            ┃
┃▓▓▓▓▓▓ ▓    ▓▓▓    ▓ ▓▓   ▓▓▓▓ ▓┃    ┃▓▓▓▓▓▓     ▓▓▓▓    ▓▓           ┃
┃▓▓▓▓▓▓   ▓▓▓▓▓ ▓ ▓ ▓▓   ▓▓  ▓ ▓ ┃    ┃▓▓▓▓▓▓   ▓▓▓▓▓▓    ▓▓░          ┃
┃▓▓      ▓▓ ▓▓       ▓▓ ▓ ▓  ▓   ┃    ┃▓▓      ▓▓▓▓▓▓▓    ▓▓░░         ┃
┃ ▓ ▓▓▓  ▓  ▓▓▓▓▓   ▓  ▓       ▓▓┃    ┃   ▓▓▓  ▓▓▓▓▓▓▓               ▓▓┃
┃   ▓ ▓▓ ▓▓ ▓▓▓  ▓ ▓▓  ▓▓▓ ▓ ▓ ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓      ▓▓┃
┃  ▓▓▓▓▓  ▓▓▓ ▓▓▓▓  ▓▓▓▓   ▓ ▓ ▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓   ┃
┃  ▓▓▓  ▓▓   ▓▓▓ ▓  ▓▓▓ ▓ ▓▓▓▓ ▓ ┃    ┃  ▓▓▓▓▓▓▓    ▓▓▓   ▓▓▓▓   ▓▓▓   ┃
┃ ▓▓ ▓▓▓▓▓    ▓▓▓   ▓▓▓ ▓  ▓     ┃    ┃  ▓▓▓▓▓▓▓    ▓▓    ▓▓▓   ▓▓▓    ┃
┃▓ ▓   ▓▓  ▓   ▓     ▓   ▓▓▓ ▓   ┃    ┃      ▓▓▓           ░░   ▓▓     ┃
┃ ▓ ▓▓ ▓▓▓▓ ▓ ▓  ▓ ▓ ▓ ▓    ▓   ▓┃    ┃      ▓▓▓           ░░          ┃
┃ ▓▓ ▓  ▓      ▓      ▓▓▓▓▓   ▓▓▓┃    ┃                    ▓▓▓▓▓▓    ▓▓┃
┃         ▓     ▓    ▓▓   ▓▓   ▓▓┃    ┃                    ▓▓▓▓▓▓    ▓▓┃
┃  ▓▓▓▓   ▓ ▓  ▓▓ ▓ ▓▓  ▓▓▓ ▓ ▓  ┃    ┃   ▓▓▓              ▓▓▓▓▓▓▓     ┃
┃  ▓ ▓▓▓  ▓▓ ▓▓ ▓ ▓  ▓▓▓▓▓▓▓▓    ┃    ┃   ▓▓▓▓     ▓▓▓▓▓   ▓▓▓▓▓▓▓     ┃
┃    ▓ ▓ ▓▓  ▓▓ ▓▓ ▓▓  ▓         ┃    ┃     ▓▓     ▓▓▓▓▓    ▓▓▓▓▓▓     ┃
┃▓▓▓  ▓▓     ▓▓ ▓▓    ▓▓▓▓▓ ▓▓▓  ┃    ┃            ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓  ┃
┃  ▓▓      ▓▓▓ ▓▓  ▓ ▓ ▓ ▓ ▓ ▓▓▓▓┃    ┃          ▓▓▓▓▓▓     ▓▓▓░▓▓▓▓▓▓ ┃
┃▓      ▓▓ ▓▓  ▓  ▓▓ ▓▓ ▓   ▓ ▓▓ ┃    ┃        ▓▓▓▓▓    ▓▓▓▓▓▓  ▓▓▓▓▓▓▓┃
┃▓▓▓▓▓▓  ▓▓▓ ▓▓   ▓▓▓  ▓  ▓▓▓▓▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓  ▓▓▓▓▓▓▓┃
┃     ▓▓▓▓   ▓  ▓▓▓ ▓▓▓▓ ▓▓▓  ▓ ▓┃    ┃    ▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃    ▓     ▓ ▓  ▓▓▓ ▓▓▓ ▓▓ ▓ ▓▓▓ ┃    ┃               ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓    ▓▓  ▓     ▓▓       ▓▓ ▓  ┃    ┃                ▓▓       ▓▓▓▓▓▓ ┃
┃▓ ▓  ▓▓ ▓▓  ▓▓  ▓▓  ▓   ▓▓  ▓▓▓▓┃    ┃     ▓▓▓                 ▓▓▓▓▓▓ ┃
┃ ▓   ▓▓  ▓  ▓    ▓  ▓ ▓▓ ▓ ▓▓   ┃    ┃     ▓▓▓                  ▓▓▓▓▓ ┃
┃▓  ▓ ▓ ▓▓  ▓▓▓    ▓  ▓ ▓  ▓▓▓▓▓▓┃    ┃           ▓▓              ▓▓▓▓ ┃
┃▓ ▓▓     ▓ ▓  ▓  ▓   ▓  ▓▓   ▓  ┃    ┃  ▓▓       ▓▓                ▓▓ ┃
┃ ▓▓▓ ▓  ▓  ▓▓ ▓  ▓▓  ▓ ▓ ▓▓  ▓▓▓┃    ┃  ▓▓                         ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓ ▓   ▓▓▓  ▓ ▓▓▓ ▓▓▓▓▓▓    ▓  ▓┃    ┃       ▓▓     ▓▓▓▓              ┃
┃   ▓ ▓ ▓▓ ▓▓ ▓ ▓▓▓   ▓    ▓ ▓ ▓ ┃    ┃       ▓▓     ▓▓▓▓          ▓▓  ┃
┃▓ ▓▓ ▓▓   ▓   ▓▓▓▓ ▓▓ ▓  ▓▓ ▓▓  ┃    ┃ ▓▓▓  ▓▓      ▓▓▓▓       ▓▓▓▓▓▓ ┃
┃ ▓▓    ▓▓  ▓▓ ▓▓▓    ▓ ▓▓▓▓▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓      ▓▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃▓▓ ▓ ▓▓▓ ▓▓   ▓▓▓▓   ▓  ▓▓▓ ▓ ▓▓┃    ┃ ▓▓▓▓▓▓▓      ▓▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃  ▓ ▓▓ ▓  ▓▓ ▓ ▓▓▓   ▓ ▓▓▓▓▓ ▓▓▓┃    ┃    ▓▓▓    ▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃ ▓▓  ▓  ▓ ▓ ▓▓▓▓▓ ▓  ▓ ▓▓▓ ▓  ▓▓┃    ┃     ▓     ▓▓▓▓▓▓▓     ▓▓▓▓▓  ▓▓┃
┃   ▓ ▓▓    ▓▓  ▓   ▓▓  ▓  ▓ ▓ ▓▓┃    ┃     ▓     ▓▓▓▓▓▓▓     ▓▓▓▓▓  ▓▓┃
┃     ▓ ▓▓▓ ▓ ▓▓▓▓▓▓   ▓▓ ▓ ▓▓  ▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓   ┃
┃ ▓  ▓▓▓ ▓▓▓      ▓▓  ▓▓▓▓▓ ▓▓  ▓┃    ┃    ▓▓▓▓▓▓░░   ▓▓▓▓  ▓▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓▓▓  ▓ ▓   ▓▓   ▓▓▓   ▓▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓░    ▓▓▓  ▓▓▓         ┃
┃▓▓  ▓ ▓ ▓▓▓ ▓ ▓▓ ▓  ▓ ▓      ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓     ▓▓░  ▓▓▓      ▓▓ ┃
┃▓▓ ▓   ▓▓   ▓▓  ▓▓▓▓▓▓ ▓▓ ▓▓ ▓▓▓┃    ┃▓▓  ▓░▓        ░░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓  ▓▓▓ ▓ ▓▓  ▓▓  ▓ ▓▓ ▓▓▓▓▓  ▓▓┃    ┃▓▓  ▓▓▓         ░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓ ▓▓▓   ▓ ▓  ▓▓ ▓▓▓▓  ▓▓  ▓▓▓ ┃    ┃▓▓  ▓▓▓          ░▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓   ▓▓▓  ▓ ▓▓  ▓ ▓   ▓ ▓▓▓▓▓  ▓ ┃    ┃▓▓  ▓▓▓   ▓▓▓           ▓▓▓▓▓▓▓ ┃
┃▓ ▓      ▓▓▓▓ ▓  ▓      ▓   ▓▓ ▓┃    ┃▓▓       ▓▓▓▓           ▓▓▓▓▓▓▓ ┃
┃▓▓▓▓  ▓ ▓▓  ▓  ▓  ▓▓ ▓▓  ▓▓▓▓▓▓▓┃    ┃▓▓▓▓   ▓▓▓▓▓▓            ▓▓▓▓▓▓ ┃
┃▓  ▓ ▓ ▓▓ ▓ ▓     ▓ ▓ ▓ ▓▓▓ ▓  ▓┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓      ▓▓▓▓  ▓▓▓▓   ┃
┃▓▓▓▓ ▓▓▓ ▓▓ ▓▓▓ ▓ ▓ ▓▓▓    ▓    ┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓▓    ▓▓▓▓         ┃
┃   ▓    ▓▓▓ ▓▓▓  ▓▓ ▓▓▓  ▓  ▓▓▓ ┃    ┃  ▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓     ▓▓  ┃
┃  ▓▓▓ ▓▓ ▓ ▓▓▓ ▓▓   ▓  ▓▓ ▓ ▓▓ ▓┃    ┃  ▓▓      ▓▓▓▓▓▓▓           ▓▓  ┃
┃ ▓▓▓      ▓    ▓  ▓   ▓▓  ▓ ▓▓▓ ┃    ┃ ▓▓▓       ▓▓▓▓▓▓           ▓▓  ┃
┃ ▓  ▓ ▓▓ ▓▓ ▓▓ ▓▓▓▓      ▓▓     ┃    ┃ ▓         ▓▓▓▓▓▓               ┃
┃▓▓  ▓  ▓   ▓▓▓▓▓▓    ▓▓▓▓   ▓▓  ┃    ┃▓▓         ▓▓▓▓▓▓               ┃
┃▓▓▓    ▓▓  ▓▓  ▓▓            ▓▓▓┃    ┃▓▓     ▓▓  ▓▓▓▓▓▓               ┃
┃▓  ▓   ▓▓  ▓▓▓ ▓  ▓  ▓  ▓      ▓┃    ┃▓▓     ▓▓  ▓▓▓▓▓                ┃
┃▓▓ ▓   ▓▓  ▓▓▓▓▓ ▓    ▓▓ ▓▓▓ ▓  ┃    ┃▓▓▓    ▓▓  ▓▓▓▓▓      ▓▓▓▓▓     ┃
┃▓▓ ▓▓▓  ▓ ▓▓▓ ▓  ▓▓ ▓ ▓▓▓▓ ▓ ▓  ┃    ┃▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓     ┃
┃▓ ▓ ▓ ▓ ▓  ▓▓ ▓▓▓▓▓▓▓ ▓ ▓     ▓ ┃    ┃  ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓     ┃
┃ ▓ ▓▓ ▓▓  ▓ ▓▓▓▓    ▓ ▓▓▓▓▓▓ ▓▓ ┃    ┃   ▓▓▓▓    ▓▓▓▓▓▓     ▓▓▓▓▓     ┃
┃  ▓▓ ▓ ▓  ▓▓▓▓  ▓  ▓  ▓  ▓ ▓   ▓┃    ┃   ▓▓▓     ▓▓▓                  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓▓▓    ▓ ▓▓ ▓▓▓▓ ▓▓ ▓ ▓     ▓┃    ┃  ▓▓▓▓       ▓▓▓▓▓▓             ┃
┃▓ ▓▓▓▓ ▓▓▓   ▓▓▓ ▓▓        ▓▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓             ┃
┃  ▓ ▓ ▓▓ ▓▓▓  ▓ ▓▓ ▓▓   ▓ ▓ ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓             ┃
┃▓▓ ▓▓▓ ▓▓▓▓ ▓▓▓▓ ▓    ▓▓  ▓ ▓  ▓┃    ┃  ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓             ┃
┃  ▓▓  ▓▓ ▓▓▓     ▓▓▓▓▓▓ ▓      ▓┃    ┃  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓       ┃
┃▓▓ ▓▓▓ ▓▓▓▓   ▓   ▓  ▓ ▓▓▓▓   ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓      ┃
┃▓   ▓▓▓   ▓  ▓ ▓▓▓▓ ▓▓ ▓▓▓      ┃    ┃ ▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓      ┃
┃ ▓▓ ▓▓▓▓▓ ▓ ▓▓ ▓ ▓▓▓▓ ▓  ▓  ▓   ┃    ┃ ▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓▓▓     ▓  ▓▓▓▓ ▓ ▓ ▓ ▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓  ▓▓▓▓   ┃
┃   ▓  ▓ ▓   ▓     ▓  ▓▓  ▓▓▓ ▓  ┃    ┃  ░░░            ▓▓▓▓    ▓▓▓▓   ┃
┃  ▓ ▓    ▓▓▓▓   ▓▓  ▓   ▓▓ ▓  ▓▓┃    ┃   ░░    ▓▓▓▓    ▓▓▓▓    ▓▓     ┃
┃ ▓ ▓▓ ▓  ▓ ▓ ▓▓  ▓▓▓▓▓▓   ▓     ┃    ┃   ▓▓▓   ▓▓▓▓  ▓▓▓▓▓▓           ┃
┃▓  ▓▓▓▓▓ ▓▓▓  ▓▓▓  ▓  ▓ ▓     ▓ ┃    ┃   ▓▓▓▓  ▓▓▓  ▓▓▓▓▓▓▓           ┃
┃ ▓  ▓  ▓ ▓  ▓  ▓▓ ▓▓▓     ▓ ▓  ▓┃    ┃    ▓▓▓  ▓▓▓  ▓▓▓▓▓▓▓           ┃
┃▓▓  ▓▓▓  ▓▓▓▓ ▓  ▓ ▓ ▓▓▓ ▓ ▓▓   ┃    ┃    ▓▓▓  ▓▓▓▓   ▓▓▓▓▓▓          ┃
┃ ▓▓  ▓▓ ▓▓▓ ▓   ▓▓▓▓ ▓  ▓▓▓ ▓▓ ▓┃    ┃    ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓   ▓▓ ▓ ▓▓▓▓ ▓▓▓▓▓▓▓ ▓ ▓▓ ▓▓   ┃    ┃    ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃   ▓▓▓▓▓▓▓▓▓▓▓ ▓    ▓▓ ▓ ▓ ▓ ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓░   ▓▓▓▓▓▓▓▓▓▓    ┃
┃  ▓▓▓▓ ▓▓  ▓▓ ▓ ▓ ▓▓   ▓ ▓  ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓░   ▓▓▓▓▓▓▓▓      ┃
┃▓ ▓▓     ▓▓▓▓▓    ▓▓ ▓▓▓▓ ▓▓ ▓ ▓┃    ┃  ▓▓     ▓▓▓▓▓░   ▓▓▓▓▓▓▓▓      ┃
┃   ▓     ▓  ▓ ▓ ▓▓▓  ▓▓▓▓▓    ▓ ┃    ┃  ▓▓     ▓▓▓▓▓░      ▓▓▓▓▓      ┃
┃▓ ▓▓▓▓  ▓▓▓ ▓▓▓      ▓▓  ▓ ▓    ┃    ┃  ▓▓     ▓▓▓▓▓▓      ▓▓▓▓▓▓     ┃
┃▓ ▓▓  ▓  ▓  ▓  ▓▓  ▓ ▓▓▓▓▓▓▓▓▓▓ ┃    ┃▓▓▓▓     ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓▓  ▓▓ ▓▓▓ ▓ ▓▓▓ ▓▓ ▓▓  ▓▓▓   ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓  ┃
┃▓  ▓   ▓▓▓ ▓▓▓▓ ▓▓ ▓  ▓  ▓   ▓▓ ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓  ▓▓  ┃
┃▓▓▓▓ ▓  ▓▓  ▓▓  ▓     ▓▓ ▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓     ▓▓▓▓  ▓▓  ┃
┃▓ ▓▓▓▓  ▓▓▓ ▓  ▓▓ ▓▓  ▓▓▓ ▓   ▓ ┃    ┃▓▓▓▓▓   ▓▓▓▓▓  ▓▓     ▓▓▓▓▓     ┃
┃▓▓   ▓ ▓   ▓▓  ▓▓   ▓▓▓▓▓▓▓   ▓▓┃    ┃▓▓▓     ▓  ▓▓  ▓▓   ▓▓▓▓▓▓▓     ┃
┃▓▓▓   ▓▓▓  ▓  ▓▓    ▓   ▓▓▓▓▓▓  ┃    ┃▓▓▓   ▓▓▓  ▓        ▓▓▓▓▓▓▓▓    ┃
┃▓▓ ▓▓ ▓▓ ▓▓▓   ▓ ▓ ▓▓▓▓  ▓ ▓    ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓    ┃
┃ ▓ ▓▓▓▓  ▓▓▓ ▓▓    ▓  ▓ ▓▓ ▓  ▓▓┃    ┃▓▓▓▓▓▓▓  ▓▓▓       ▓▓    ▓▓▓    ┃
┃▓▓▓▓ ▓▓  ▓ ▓  ▓ ▓▓▓▓▓  ▓ ▓ ▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓                         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓▓      ▓    ▓ ▓  ▓    ▓▓     ┃    ┃ ▓▓                      ▓▓     ┃
┃▓▓▓  ▓  ▓ ▓▓▓ ▓▓ ▓▓▓▓  ▓ ▓▓▓  ▓ ┃    ┃▓▓▓       ▓▓▓    ▓▓▓▓   ▓▓▓▓    ┃
┃▓▓▓  ▓▓ ▓ ▓▓▓▓   ▓ ▓▓▓▓▓▓  ▓▓ ▓ ┃    ┃▓▓▓     ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃ ▓ ▓▓▓  ▓▓ ▓  ▓  ▓ ▓▓   ▓▓ ▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓ ▓▓ ▓▓▓ ▓▓  ▓  ▓ ▓▓▓ ▓▓ ▓  ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓▓   ▓▓ ▓▓ ▓  ▓▓ ▓▓▓▓  ▓  ▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓      ┃
┃     ▓▓▓ ▓▓▓▓   ▓▓   ▓▓▓▓▓▓   ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓   ▓▓   ▓▓▓▓▓      ┃
┃   ▓ ▓▓▓  ▓▓  ▓▓▓ ▓   ▓▓ ▓  ▓   ┃    ┃    ▓▓▓▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓      ┃
┃   ▓▓▓ ▓▓  ▓▓ ▓▓▓▓  ▓▓  ▓  ▓▓▓ ▓┃    ┃   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓  ┃
┃▓▓▓▓ ▓   ▓▓▓▓▓    ▓  ▓▓  ▓▓ ▓▓ ▓┃    ┃   ▓▓  ▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓  ┃
┃       ▓▓  ▓ ▓▓ ▓▓▓▓▓ ▓▓▓▓▓  ▓  ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ┃
┃▓▓   ▓ ▓▓ ▓    ▓  ▓       ▓ ▓  ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓          ▓▓   ┃
┃▓ ▓ ▓ ▓▓▓▓▓▓▓▓▓▓▓ ▓ ▓▓▓    ▓▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓     ▓▓   ┃
┃▓ ▓▓▓▓▓  ▓▓  ▓ ▓▓   ▓  ▓▓  ▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓   ┃
┃▓▓▓  ▓▓▓ ▓ ▓▓▓▓▓ ▓▓ ▓▓▓  ▓▓   ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ░  ┃
┃▓  ▓ ▓▓ ▓   ▓▓ ▓ ▓▓▓  ▓▓     ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓          ▓▓▓┃
┃ ▓▓▓▓    ▓  ▓ ▓ ▓▓       ▓▓ ▓▓ ▓┃    ┃ ▓▓▓   ▓▓   ▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓┃
┃▓  ▓   ▓▓  ▓▓▓▓▓ ▓▓ ▓▓▓ ▓▓▓ ▓ ▓▓┃    ┃  ▓▓   ▓▓   ▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓┃
┃▓ ▓▓  ▓▓▓▓ ▓    ▓ ▓▓ ▓  ▓ ▓▓ ▓▓▓┃    ┃       ▓▓       ▓▓▓▓    ▓▓▓▓▓▓▓▓┃
┃    ▓▓ ▓▓       ▓▓▓  ▓  ▓   ▓▓▓▓┃    ┃       ▓▓       ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓┃
┃      ▓ ▓  ▓ ▓ ▓▓  ▓ ▓▓▓  ▓▓▓▓  ┃    ┃       ░░          ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓    ▓   ▓▓ ▓  ▓▓ ▓▓▓▓▓▓ ▓▓ ┃    ┃       ░░          ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓   ▓▓▓▓▓▓▓▓ ▓ ▓ ▓▓ ▓▓  ▓ ▓▓▓▓ ▓┃    ┃       ░▓▓▓▓▓▓  ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓    ▓ ▓▓▓    ▓▓▓  ▓▓▓ ▓ ▓ ▓ ┃    ┃        ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓   ▓    ▓▓ ▓▓ ▓▓   ▓▓▓  ▓▓▓  ▓ ┃    ┃        ▓▓▓▓▓▓      ▓▓▓    ░░░░ ┃
┃  ▓  ▓▓ ▓    ▓  ▓  ▓ ▓    ▓ ▓ ▓ ┃    ┃     ▓▓▓▓▓▓▓   ▓▓   ▓▓▓    ░░░░ ┃
┃▓▓ ▓▓ ▓▓▓▓▓ ▓  ▓▓   ▓ ▓▓▓    ▓ ▓┃    ┃    ▓▓▓▓▓▓▓    ▓▓   ▓▓▓▓▓  ░░░░ ┃
┃▓   ▓▓▓▓▓▓ ▓▓ ▓▓▓   ▓▓ ▓▓▓▓▓▓▓▓▓┃    ┃   ░▓▓▓▓▓▓     ▓▓   ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓ ▓▓▓ ▓▓      ▓  ▓▓▓   ▓▓  ▓ ┃    ┃  ░░▓▓▓▓▓▓          ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓  ▓▓▓      ▓  ▓  ▓▓▓▓ ▓ ▓▓ ▓┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓   ▓ ▓ ▓▓ ▓ ▓▓ ▓▓  ▓▓ ▓▓  ▓▓ ┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓▓▓  ▓ ▓▓ ▓      ▓  ▓▓▓ ▓  ▓┃    ┃                         ▓▓     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓▓▓▓▓▓▓▓▓ ▓   ▓▓  ▓   ▓▓▓ ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓            ▓▓▓▓   ┃
┃ ▓  ▓     ▓▓▓ ▓▓  ▓▓▓▓▓▓ ▓ ▓▓▓ ▓┃    ┃   ▓▓     ▓▓▓▓    ▓▓▓▓   ▓▓▓▓   ┃
┃   ▓▓       ▓▓ ▓▓ ▓ ▓    ▓  ▓ ▓ ┃    ┃   ▓▓     ▓▓▓▓▓   ▓▓▓▓▓  ▓      ┃
┃  ▓▓   ▓▓▓▓▓▓ ▓▓  ▓▓▓▓▓ ▓▓▓     ┃    ┃   ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓  ▓▓ ▓  ▓  ▓▓ ▓▓   ▓▓▓▓▓   ▓  ▓┃    ┃   ▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓ ▓  ▓      ▓▓▓▓▓▓ ▓ ▓▓ ▓ ▓▓▓   ┃    ┃    ▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓ ▓ ▓▓▓   ▓▓▓▓ ▓▓ ▓ ▓    ▓   ▓▓▓┃    ┃    ▓▓      ▓▓▓▓▓▓░░░   ▓▓      ┃
┃  ▓ ▓▓ ▓▓ ▓    ▓▓  ▓  ▓ ▓▓      ┃    ┃    ▓▓▓        ▓▓  ░░   ▓▓      ┃
┃ ▓   ▓   ▓▓  ▓▓ ▓   ▓▓  ▓ ▓▓▓ ▓ ┃    ┃    ▓▓▓            ░░   ▓▓▓▓▓   ┃
┃▓ ▓▓ ▓▓▓▓ ▓    ▓   ▓ ▓ ▓ ▓▓ ▓ ▓▓┃    ┃    ▓▓▓▓▓           ░   ▓▓▓▓▓   ┃
┃  ▓ ▓▓▓▓▓▓     ▓ ▓▓ ▓ ▓  ▓ ▓▓   ┃    ┃    ▓▓▓▓▓                 ░░░   ┃
┃  ▓  ▓▓▓▓ ▓ ▓▓▓  ▓ ▓   ▓    ▓   ┃    ┃     ▓▓▓▓                 ░░░   ┃
┃  ▓ ▓  ▓ ▓     ▓ ▓ ▓ ▓ ▓ ▓▓▓   ▓┃    ┃     ▓▓▓▓      ▓▓▓    ▓▓▓▓▓▓▓   ┃
┃▓  ▓ ▓ ▓▓   ▓▓▓▓ ▓   ▓▓▓▓▓▓ ▓▓▓▓┃    ┃     ░░      ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓┃
┃    ▓ ▓    ▓ ▓▓ ▓▓▓ ▓   ▓   ▓▓▓▓┃    ┃     ░░      ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓┃
┃▓ ▓  ▓▓   ▓▓  ▓ ▓▓▓▓ ▓▓▓▓▓  ▓▓  ┃    ┃      ░      ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓  ┃
┃  ▓  ▓ ▓ ▓▓  ▓ ▓▓▓▓ ▓ ▓ ▓    ▓ ▓┃    ┃      ▓▓▓▓▓   ▓▓▓▓▓▓▓▓░░░░      ┃
┃▓▓ ▓▓ ▓▓▓▓▓  ▓ ▓  ▓▓▓  ▓ ▓  ▓  ▓┃    ┃▓▓    ▓▓▓▓▓   ▓▓▓▓▓▓▓  ░░░      ┃
┃▓▓▓    ▓  ▓   ▓▓ ▓▓▓    ▓▓▓ ▓ ▓ ┃    ┃▓▓▓   ▓▓      ▓▓▓▓▓▓▓  ░░░      ┃
┃ ▓  ▓ ▓▓   ▓ ▓ ▓ ▓▓ ▓▓▓▓    ▓   ┃    ┃▓▓▓   ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓ ▓ ▓    ▓▓▓▓  ▓▓ ▓▓▓▓▓▓▓ ▓▓┃    ┃ ▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓▓░    ┃
┃ ▓▓▓▓   ▓▓    ▓▓ ▓ ▓  ▓ ▓ ▓  ▓ ▓┃    ┃ ▓▓▓▓         ▓▓▓▓    ▓▓▓       ┃
┃ ▓▓   ▓▓▓      ▓  ▓▓  ▓▓      ▓ ┃    ┃ ▓▓▓▓         ▓▓▓▓    ▓▓        ┃
┃▓ ▓▓▓   ▓   ▓ ▓▓▓▓     ▓   ▓▓▓  ┃    ┃ ▓▓▓▓         ▓▓▓▓              ┃
┃    ▓▓   ▓▓▓▓▓ ▓ ▓   ▓  ▓▓▓    ▓┃    ┃  ▓▓▓▓    ▓▓▓▓▓▓▓▓      ▓▓      ┃
┃ ▓▓▓▓▓    ▓▓▓  ▓ ▓▓  ▓ ▓▓ ▓    ▓┃    ┃   ▓▓▓    ▓▓▓▓▓▓▓▓      ▓▓      ┃
┃   ▓ ▓   ▓   ▓▓▓▓▓ ▓▓    ▓  ▓▓▓▓┃    ┃    ▓▓     ▓▓▓▓▓▓▓          ▓▓▓▓┃
┃▓▓   ▓   ▓ ▓▓▓▓▓ ▓  ▓    ▓ ▓▓▓▓▓┃    ┃    ▓▓     ▓▓▓▓▓▓           ▓▓▓▓┃
┃ ▓▓▓▓▓ ▓ ▓ ▓   ▓    ▓▓  ▓   ▓▓ ▓┃    ┃ ▓▓▓▓▓      ▓▓▓▓▓   ▓▓      ▓▓▓▓┃
┃ ▓▓ ▓ ▓  ▓  ▓ ▓▓▓▓▓▓ ▓▓ ▓      ▓┃    ┃ ▓▓▓▓▓         ▓▓▓▓▓▓▓      ▓▓▓▓┃
┃▓ ▓▓▓▓▓ ▓▓ ▓    ▓▓ ▓▓▓ ▓ ▓ ▓ ▓▓▓┃    ┃ ▓▓▓▓▓  ▓▓     ▓▓▓▓▓▓▓      ▓▓▓▓┃
┃▓▓  ▓▓  ▓▓ ▓   ▓▓▓▓  ▓    ▓▓▓▓▓ ┃    ┃    ▓▓  ▓▓      ▓▓          ▓▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓    ▓▓ ▓▓▓▓▓▓ ▓▓▓ ▓▓ ▓▓▓▓  ▓ ┃    ┃             ▓▓                 ┃
┃      ▓   ▓   ▓   ▓   ▓▓ ▓  ▓   ┃    ┃             ▓▓░░▓▓▓▓▓▓▓▓▓      ┃
┃▓▓  ▓ ▓ ▓▓   ▓▓▓ ▓▓▓ ▓▓ ▓ ▓     ┃    ┃      ▓▓▓▓▓  ░░░░▓▓▓▓▓▓▓▓▓      ┃
┃▓ ▓▓▓ ▓▓ ▓▓▓▓ ▓ ▓▓ ▓▓▓ ▓▓   ▓ ▓▓┃    ┃▓▓░░░░▓▓▓▓▓░░░░░░▓▓▓▓▓▓▓▓▓      ┃
┃▓▓  ▓▓ ▓ ▓   ▓   ▓     ▓▓▓ ▓▓  ▓┃    ┃▓▓░░░░▓▓▓▓▓░░░         ▓▓▓▓▓▓   ┃
┃ ▓▓   ▓ ▓▓▓ ▓       ▓ ▓▓ ▓ ▓▓  ▓┃    ┃▓▓   ▓▓▓▓▓▓▓░░         ▓▓▓▓▓▓   ┃
┃▓▓  ▓▓▓ ▓ ▓  ▓ ▓▓▓▓▓   ▓ ▓ ▓ ▓▓▓┃    ┃     ▓▓▓▓▓▓▓▓░ ▓▓      ▓▓▓▓▓▓   ┃
┃      ▓  ▓ ▓▓▓ ▓▓     ▓▓▓▓ ▓    ┃    ┃     ▓▓▓▓░▓▓▓▓ ▓▓      ▓▓▓▓▓▓   ┃
┃▓   ▓▓▓▓▓▓ ▓▓▓      ▓   ▓ ▓▓▓ ▓▓┃    ┃     ▓▓▓▓░░▓▓▓         ▓▓▓▓▓▓   ┃
┃  ▓▓   ▓    ▓ ▓▓    ▓▓▓▓ ▓  ▓  ▓┃    ┃       ▓▓           ▓▓▓▓   ░░   ┃
┃ ▓ ▓▓  ▓▓       ▓▓ ▓ ▓▓▓   ▓ ▓  ┃    ┃       ▓▓       ▓▓  ▓▓▓▓   ░░   ┃
┃▓     ▓▓▓▓ ▓   ▓▓▓ ▓▓     ▓▓▓▓▓▓┃    ┃      ▓▓▓▓▓     ▓▓ ▓▓▓     ▓▓▓▓▓┃
┃▓▓▓   ▓▓▓▓▓▓     ▓ ▓▓▓▓  ▓ ▓  ▓▓┃    ┃▓▓▓   ▓▓▓▓▓▓    ▓▓ ▓▓▓     ▓▓▓▓▓┃
┃▓▓▓  ▓▓▓  ▓▓▓   ▓▓   ▓ ▓   ▓▓▓▓ ┃    ┃▓▓▓   ▓▓  ▓▓    ▓▓   ▓▓    ▓▓▓▓ ┃
┃▓▓ ▓▓ ▓▓  ▓   ▓ ▓ ▓▓ ▓▓▓▓    ▓▓ ┃    ┃▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓ ▓▓▓▓  ▓▓▓▓ ┃
┃▓ ▓ ▓▓ ▓ ▓▓▓    ▓▓▓▓ ▓▓▓▓▓ ▓▓   ┃    ┃   ▓▓▓▓▓  ▓▓    ▓▓▓▓ ▓▓▓▓▓▓▓▓▓  ┃
┃   ▓   ▓  ▓▓▓  ▓ ▓▓  ▓ ▓▓▓▓▓▓▓  ┃    ┃         ▓▓▓    ▓▓▓  ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓ ▓ ▓▓▓▓  ▓   ▓ ▓ ▓▓▓▓▓  ▓ ▓┃    ┃      ▓▓▓▓▓▓    ▓▓▓  ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓ ▓▓▓  ▓▓ ▓▓ ▓ ▓▓ ▓ ▓ ▓ ▓▓  ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓ ▓▓▓▓ ▓▓▓▓   ▓ ▓▓▓▓ ▓  ▓▓▓ ▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓   ▓▓▓▓▓▓┃
┃▓ ▓   ▓▓▓▓▓▓▓▓    ▓▓  ▓▓   ▓▓   ┃    ┃    ▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓   ▓▓▓▓  ┃
┃  ▓▓▓▓ ▓▓ ▓ ▓▓▓▓▓   ▓ ▓   ▓▓ ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓       ▓▓  ▓▓▓▓  ┃
┃▓     ▓ ▓▓▓  ▓  ▓   ▓ ▓▓ ▓ ▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓       ▓▓  ▓▓▓▓▓ ┃
┃  ▓    ▓▓ ▓▓▓▓ ▓  ▓  ▓ ▓   ▓▓▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓ ┃
┃    ▓▓ ▓▓ ▓  ▓ ▓▓ ▓▓▓▓  ▓▓▓▓▓ ▓▓┃    ┃       ▓▓▓     ▓▓▓▓▓▓     ▓▓▓▓▓ ┃
┃ ▓▓      ▓  ▓  ▓▓ ▓▓  ▓▓   ▓▓▓  ┃    ┃               ▓▓▓▓▓▓     ▓▓▓▓▓ ┃
┃  ▓▓ ▓▓  ▓ ▓  ▓▓▓ ▓ ▓  ▓  ▓   ▓▓┃    ┃  ▓▓▓▓▓        ▓▓▓▓▓          ▓▓┃
┃ ▓ ▓▓▓▓▓▓  ▓ ▓  ▓ ▓   ▓ ▓▓ ▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓       ▓▓▓▓          ▓▓┃
┃  ▓ ▓ ▓▓▓ ▓▓ ▓  ▓▓ ▓▓ ▓  ▓  ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓        ▓▓  ┃
┃ ▓▓    ▓ ▓▓ ▓▓▓▓▓  ▓    ▓ ▓ ▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓  ┃
┃  ▓▓▓▓▓  ▓▓ ▓  ▓▓▓ ▓  ▓▓ ▓ ▓▓▓  ┃    ┃  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓  ┃
┃ ▓▓▓▓▓   ▓▓ ▓▓▓  ▓ ▓▓▓  ▓  ▓  ▓▓┃    ┃  ▓▓▓▓   ▓▓▓▓▓                  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃    ▓▓    ▓  ▓▓▓   ▓▓ ▓▓     ▓▓ ┃    ┃             ▓▓    ▓▓           ┃
┃▓▓ ▓   ▓▓   ▓▓▓ ▓  ▓▓ ▓ ▓   ▓ ▓ ┃    ┃       ▓▓    ▓▓    ▓▓           ┃
┃▓   ▓▓▓▓▓ ▓▓  ▓  ▓      ▓▓ ▓   ▓┃    ┃       ▓▓▓▓▓ ▓▓                 ┃
┃▓▓   ▓   ▓▓▓▓ ▓ ▓ ▓▓  ▓▓▓   ▓▓▓ ┃    ┃       ▓▓▓▓▓  ▓▓▓          ▓▓▓▓ ┃
┃▓ ▓▓  ▓ ▓▓ ▓  ▓ ▓▓ ▓ ▓     ▓▓ ▓ ┃    ┃      ▓▓▓▓▓   ▓▓▓▓         ▓▓▓▓ ┃
┃  ▓ ▓▓▓ ▓▓   ▓▓▓   ▓ ▓▓▓  ▓▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓   ▓▓▓▓▓▓┃
┃▓▓ ▓ ▓▓▓▓▓ ▓▓  ▓▓▓▓  ▓▓ ▓ ▓▓  ▓▓┃    ┃    ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓  ▓▓  ▓▓ ▓▓ ▓▓▓▓  ▓▓ ▓▓ ▓▓   ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓   ┃
┃  ▓  ▓▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓  ▓▓▓▓▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓    ┃
┃  ▓▓▓ ▓▓▓▓ ▓▓   ▓▓       ▓ ▓    ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓            ┃
┃ ▓▓ ▓▓▓▓▓ ▓▓▓     ▓ ▓▓      ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓           ┃
┃  ▓ ▓ ▓   ▓  ▓▓ ▓ ▓▓▓ ▓▓▓ ▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓  ▓▓▓▓▓    ▓▓▓▓▓░▓▓▓▓ ▓▓┃
┃   ▓▓ ▓▓  ▓▓ ▓▓ ▓    ▓▓▓ ▓ ▓▓ ▓▓┃    ┃  ▓▓▓▓▓   ▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓ ▓▓┃
┃ ▓▓ ▓▓   ▓ ▓▓    ▓▓ ▓▓  ▓ ▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓    ▓▓        ▓▓  ▓▓▓▓▓   ┃
┃ ▓▓▓ ▓ ▓▓▓ ▓  ▓ ▓▓  ▓▓   ▓▓    ▓┃    ┃ ▓▓▓▓▓ ▓▓▓▓         ▓▓  ▓▓▓▓    ┃
┃ ▓  ▓▓ ▓ ▓▓    ▓ ▓▓  ▓ ▓▓ ▓▓▓   ┃    ┃ ▓▓▓▓▓ ▓▓▓▓     ▓▓▓▓▓░▓▓▓▓▓▓    ┃
┃▓▓ ▓▓  ▓▓▓    ▓ ▓▓  ▓  ▓▓▓▓▓  ▓▓┃    ┃▓▓     ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓┃
┃▓▓    ▓▓▓▓▓   ▓  ▓▓▓▓▓▓  ▓    ▓▓┃    ┃▓▓    ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓    ▓▓┃
┃ ▓ ▓▓▓▓▓▓ ▓▓▓▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓▓    ▓   ▓▓▓▓ ▓ ▓ ▓    ▓  ▓┃    ┃▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓          ┃
┃▓ ▓▓▓ ▓▓    ▓ ▓ ▓▓▓ ▓▓  ▓▓ ▓   ▓┃    ┃▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓          ┃
┃▓ ▓▓▓▓▓  ▓▓     ▓  ▓▓▓▓ ▓ ▓ ▓   ┃    ┃▓▓▓▓▓▓▓         ▓▓▓▓▓▓   ░      ┃
┃▓▓▓▓  ▓ ▓ ▓▓ ▓  ▓▓ ▓▓    ▓▓  ▓  ┃    ┃▓▓▓▓▓              ▓▓▓   ▓▓     ┃
┃▓▓▓ ▓      ▓ ▓     ▓▓ ▓  ▓▓     ┃    ┃▓▓▓▓▓              ▓▓▓   ▓▓     ┃
┃ ▓ ▓▓    ▓   ▓ ▓ ▓ ▓▓▓▓▓  ▓ ▓▓ ▓┃    ┃  ░░              ▓▓▓▓   ▓▓▓▓▓  ┃
┃▓     ▓▓▓▓▓ ▓▓ ▓ ▓▓▓▓   ▓ ▓▓▓▓ ▓┃    ┃  ░░  ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓▓  ▓   ▓ ▓▓▓  ▓▓▓▓▓▓▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓  ▓▓  ▓ ▓▓▓ ▓▓▓ ▓ ▓▓▓▓▓▓▓▓▓▓┃    ┃  ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓▓ ▓▓   ▓▓   ▓ ▓▓▓▓   ▓▓     ┃    ┃  ▓▓  ▓▓        ▓▓▓▓▓▓   ▓▓▓    ┃
┃  ▓   ▓   ▓   ▓ ▓ ▓▓▓ ▓   ▓ ▓ ▓▓┃    ┃                ▓▓▓▓▓      ░    ┃
┃▓▓  ▓  ▓ ▓▓▓    ▓  ▓    ▓  ▓    ┃    ┃                ▓▓▓▓▓           ┃
┃▓ ▓▓ ▓ ▓   ▓ ▓▓▓▓▓▓▓▓ ▓ ▓▓▓ ▓▓▓ ┃    ┃                ▓▓▓▓            ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓    ▓ ▓▓▓  ▓ ▓ ▓▓▓▓▓▓  ▓▓▓ ▓▓ ┃    ┃                ▓▓▓▓▓     ▓▓▓▓  ┃
┃▓▓▓▓▓ ▓     ▓  ▓▓▓  ▓  ▓  ▓▓▓▓  ┃    ┃ ▓▓▓           ▓▓▓▓▓▓     ▓▓▓▓  ┃
┃ ▓▓▓  ▓ ▓▓ ▓   ▓▓ ▓ ▓  ▓ ▓   ▓ ▓┃    ┃ ▓▓▓           ▓▓▓  ▓     ░░░░  ┃
┃▓ ▓  ▓▓▓  ▓▓▓   ▓   ▓▓    ▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓              ▓▓    ░░░░  ┃
┃  ▓▓▓▓      ▓▓     ▓▓▓     ▓ ▓  ┃    ┃ ▓▓▓▓▓      ▓▓      ▓▓    ▓▓▓   ┃
┃▓ ▓     ▓▓  ▓▓  ▓▓▓ ▓     ▓▓▓ ▓ ┃    ┃        ▓▓  ▓▓            ▓▓▓   ┃
┃▓▓   ▓▓ ▓▓▓▓▓ ▓        ▓▓▓▓ ▓▓ ▓┃    ┃     ▓▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓   ┃
┃▓    ▓▓▓ ▓▓▓ ▓ ▓▓▓ ▓▓▓ ▓▓ ▓ ▓   ┃    ┃     ▓▓▓▓▓▓▓▓▓ ▓▓      ▓▓▓▓▓▓   ┃
┃     ▓▓  ▓▓▓▓  ▓▓   ▓    ▓ ▓▓ ▓ ┃    ┃     ▓▓  ▓▓▓   ▓▓  ▓▓▓   ▓▓▓▓   ┃
┃▓  ▓ ▓   ▓▓▓       ▓▓▓▓▓  ▓▓ ▓▓▓┃    ┃         ▓▓▓       ▓▓▓▓  ▓▓▓▓   ┃
┃▓▓▓    ▓  ▓  ▓ ▓   ▓ ▓   ▓▓ ▓ ▓ ┃    ┃▓▓                 ▓▓▓▓  ▓▓▓▓▓  ┃
┃▓▓     ▓  ▓     ▓ ▓▓  ▓▓ ▓▓▓▓  ▓┃    ┃▓▓                ▓▓     ▓▓▓▓▓▓ ┃
┃▓     ▓   ▓ ▓ ▓▓  ▓▓  ▓   ▓ ▓ ▓ ┃    ┃▓▓           ▓▓▓▓▓▓▓      ▓▓▓▓▓▓┃
┃▓▓ ▓   ▓ ▓ ▓▓▓ ▓▓ ▓  ▓    ▓▓▓▓ ▓┃    ┃▓▓           ▓▓▓▓▓▓▓      ▓▓▓▓▓▓┃
┃▓▓▓  ▓▓  ▓   ▓ ▓ ▓▓ ▓▓▓ ▓▓   ▓▓▓┃    ┃▓▓           ▓▓▓▓▓▓▓▓▓  ▓▓▓  ▓▓▓┃
┃▓  ▓    ▓ ▓▓ ▓▓▓▓▓▓▓▓   ▓▓▓▓  ▓▓┃    ┃             ▓▓▓▓▓▓▓▓▓  ▓▓▓   ▓▓┃
┃ ▓        ▓  ▓ ▓ ▓ ▓▓▓▓▓       ▓┃    ┃             ▓▓▓▓▓▓▓▓▓          ┃
┃▓▓▓▓▓  ▓▓   ▓▓ ▓ ▓    ▓   ▓     ┃    ┃       ▓▓   ▓▓   ▓▓             ┃
┃ ▓  ▓  ▓▓   ▓▓   ▓ ▓ ▓ ▓▓▓  ▓   ┃    ┃       ▓▓   ▓▓   ▓▓             ┃
┃  ▓  ▓▓▓▓▓   ▓▓ ▓▓▓   ▓  ▓   ▓▓ ┃    ┃       ▓▓▓  ▓▓▓▓▓▓▓   ▓▓▓    ▓▓ ┃
┃  ▓ ▓ ▓ ▓▓▓▓▓▓▓▓ ▓▓▓   ▓▓ ▓  ▓▓▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓ ┃
┃▓  ▓ ▓  ▓▓▓  ▓▓  ▓  ▓ ▓ ▓▓ ▓   ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓      ▓▓▓       ┃
┃  ▓   ▓ ▓ ▓▓▓▓▓▓     ▓▓ ▓ ▓     ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓░      ┃
┃   ▓ ▓▓▓▓ ▓▓▓ ▓▓  ▓ ▓ ▓▓  ▓▓▓▓▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓   ▓▓▓▓┃
┃▓  ▓▓  ▓ ▓  ▓▓▓▓   ▓▓ ▓▓▓   ▓▓▓▓┃    ┃   ▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓▓▓   ▓▓▓▓┃
┃▓▓ ▓▓ ▓▓ ▓  ▓     ▓▓▓ ▓▓▓▓   ▓ ▓┃    ┃   ▓▓▓▓▓▓          ▓▓▓▓▓▓    ▓▓▓┃
┃    ▓ ▓ ▓   ▓ ▓    ▓▓▓▓▓▓  ▓  ▓▓┃    ┃   ▓▓▓▓▓           ▓▓▓▓▓▓    ▓▓▓┃
┃ ▓ ▓▓ ▓▓  ▓▓  ▓▓ ▓ ▓ ▓▓▓▓▓  ▓▓ ▓┃    ┃   ▓▓▓▓▓  ▓▓▓▓▓    ▓▓▓▓▓▓       ┃
┃ ▓▓ ▓▓▓▓  ▓▓▓▓▓ ▓  ▓  ▓ ▓ ▓ ▓  ▓┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓      ▓▓▓      ┃
┃▓▓▓   ▓▓  ▓▓▓▓▓▓▓▓▓ ▓▓ ▓ ▓▓ ▓ ▓ ┃    ┃ ▓▓  ▓▓▓  ▓▓▓▓▓▓▓▓▓    ▓▓▓▓     ┃
┃ ▓▓▓ ▓▓    ▓ ▓ ▓  ▓    ▓▓▓▓  ▓ ▓┃    ┃ ▓▓  ▓▓      ▓▓▓▓▓▓    ▓▓▓▓     ┃
┃     ▓  ▓   ▓  ▓▓▓▓▓ ▓▓ ▓▓▓▓    ┃    ┃               ▓▓▓▓    ▓▓▓▓     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃    ▓▓   ▓ ▓  ▓ ▓   ▓▓▓▓   ▓▓▓▓▓┃    ┃                              ▓▓┃
┃  ▓ ▓ ▓  ▓     ▓▓ ▓  ▓   ▓▓   ▓▓┃    ┃                          ▓▓▓▓▓▓┃
┃▓    ▓  ▓       ▓  ▓  ▓   ▓▓▓ ▓▓┃    ┃                         ▓▓▓▓▓▓▓┃
┃▓▓  ▓▓  ▓▓▓▓▓▓ ▓ ▓▓▓   ▓ ▓▓▓▓  ▓┃    ┃        ▓▓▓▓▓░░   ▓▓     ▓▓▓▓   ┃
┃ ▓ ▓ ▓ ▓▓▓ ▓▓ ▓▓   ▓▓▓▓▓ ▓▓▓    ┃    ┃    ░░░░▓▓▓▓▓▓░   ▓▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓ ▓ ▓ ▓▓  ▓▓ ▓ ▓ ▓    ▓▓▓  ▓ ▓┃    ┃     ░░░▓▓▓▓▓▓░   ▓▓    ▓▓▓▓    ┃
┃ ▓  ▓ ▓ ▓▓ ▓▓ ▓▓  ▓▓    ▓▓ ▓ ▓  ┃    ┃      ░░▓▓▓▓▓▓    ▓▓    ▓▓▓▓    ┃
┃ ▓ ▓▓ ▓ ▓   ▓     ▓ ▓▓  ▓▓▓▓  ▓▓┃    ┃        ▓▓▓▓▓▓    ▓▓▓▓  ▓▓▓▓    ┃
┃▓▓▓ ▓   ▓▓▓▓▓▓▓ ▓▓ ▓▓▓▓  ▓▓  ▓ ▓┃    ┃        ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓  ▓▓  ▓      ▓   ▓   ▓▓▓▓▓▓▓▓  ┃    ┃                   ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓   ▓▓▓ ▓▓ ▓ ▓    ▓▓▓▓▓ ▓ ▓▓▓▓▓┃    ┃                   ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓ ▓ ▓   ▓   ▓ ▓ ▓▓▓▓▓▓▓ ▓  ▓▓┃    ┃  ▓▓               ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓     ▓    ▓▓  ▓▓  ▓▓▓▓  ▓▓▓▓┃    ┃  ▓▓              ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓      ▓ ▓  ▓ ▓ ▓▓▓ ▓▓▓▓▓▓   ┃    ┃  ▓▓          ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓▓▓▓ ▓▓   ▓ ▓▓ ▓ ▓▓     ▓  ▓▓ ┃    ┃  ▓▓          ▓▓▓▓▓▓▓     ▓▓▓▓  ┃
┃  ▓   ▓  ▓    ▓  ▓▓ ▓   ▓ ▓▓  ▓ ┃    ┃  ▓           ▓▓▓▓▓▓        ▓▓  ┃
┃▓▓▓  ▓▓  ▓▓▓▓▓ ▓▓ ▓         ▓▓ ▓┃    ┃▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓▓▓         ▓▓  ┃
┃▓▓  ▓▓▓ ▓▓ ▓ ▓▓ ▓▓▓     ▓  ▓▓▓  ┃    ┃▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓▓▓         ▓▓  ┃
┃  ▓▓ ▓      ▓ ▓▓  ▓  ▓▓▓ ▓  ▓▓  ┃    ┃  ▓▓▓▓       ▓▓▓▓▓▓         ▓▓  ┃
┃▓▓ ▓▓▓  ▓▓▓     ▓ ▓▓  ▓   ▓  ▓ ▓┃    ┃  ▓▓▓▓         ▓▓▓▓▓        ▓▓▓ ┃
┃    ▓▓▓  ▓     ▓  ▓▓       ▓▓▓▓▓┃    ┃  ▓▓▓▓▓  ▓▓    ░▓▓▓▓      ▓▓▓▓▓ ┃
┃▓▓ ▓▓ ▓  ▓▓▓▓▓▓▓▓ ▓▓  ▓▓▓▓▓▓  ▓ ┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓   ┃
┃▓▓▓▓ ▓▓  ▓▓ ▓▓▓▓▓  ▓  ▓ ▓ ▓ ▓   ┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓   ┃
┃▓  ▓▓▓ ▓▓▓▓▓ ▓  ▓▓▓ ▓  ▓   ▓▓▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ░  ▓▓   ┃
┃     ▓ ▓ ▓▓ ▓▓ ▓▓▓▓▓▓ ▓▓▓  ▓▓   ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ░░  ▓▓▓  ┃
┃ ▓▓▓ ▓▓▓▓▓   ▓ ▓ ▓▓▓▓  ▓    ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓  ┃
┃▓ ▓▓▓   ▓   ▓▓▓▓▓▓▓▓   ▓▓▓▓    ▓┃    ┃  ▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓   ▓▓       ┃
┃  ▓ ▓▓  ▓▓▓ ▓▓  ▓▓ ▓   ▓▓   ▓  ▓┃    ┃ ▓▓▓▓   ▓▓▓▓▓▓  ▓▓▓▓   ▓▓       ┃
┃▓▓▓    ▓▓ ▓ ▓    ▓▓ ▓▓      ▓   ┃    ┃▓▓▓     ▓▓▓▓▓                   ┃
┃▓ ▓▓     ▓▓▓▓    ▓  ▓  ▓   ▓▓   ┃    ┃▓▓▓     ▓▓▓▓▓              ▓▓   ┃
┃▓   ▓ ▓▓▓▓▓   ▓ ▓     ▓    ▓▓   ┃    ┃      ▓▓▓▓▓▓               ▓▓   ┃
┃ ▓ ▓ ▓▓▓   ▓  ▓  ▓ ▓▓▓ ▓▓▓ ▓   ▓┃    ┃      ▓▓                        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓ ▓  ▓  ▓ ▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ┃    ┃  ▓▓           ▓▓▓▓▓        ▓▓  ┃
┃  ▓▓  ▓ ▓   ▓▓  ▓▓   ▓  ▓▓ ▓ ▓  ┃    ┃  ▓▓  ▓▓       ▓▓▓▓▓        ▓▓  ┃
┃▓   ▓ ▓▓    ▓  ▓▓ ▓▓   ▓     ▓▓ ┃    ┃      ▓▓▓      ▓▓▓▓▓         ▓▓ ┃
┃▓      ▓▓   ▓  ▓   ▓ ▓▓  ▓▓  ▓▓ ┃    ┃       ▓▓         ░░         ▓▓ ┃
┃▓▓  ▓   ▓▓ ▓   ▓  ▓ ▓   ▓  ▓▓ ▓▓┃    ┃                  ░░       ▓▓▓▓ ┃
┃  ▓ ▓      ▓   ▓ ▓▓ ▓  ▓  ▓▓ ▓ ▓┃    ┃                  ░░       ▓▓▓  ┃
┃▓▓ ▓ ▓ ▓▓▓▓ ▓▓▓  ▓  ▓   ▓  ▓ ▓▓ ┃    ┃▓▓      ░   ▓▓     ░       ▓▓▓  ┃
┃▓▓ ▓  ▓ ▓ ▓ ▓  ▓  ▓▓ ▓    ▓ ▓▓  ┃    ┃▓▓     ░░   ▓▓             ▓▓▓  ┃
┃ ▓   ▓▓  ▓  ▓▓▓  ▓▓ ▓ ▓▓▓ ▓▓ ▓ ▓┃    ┃     ▓▓▓▓   ▓▓      ▓▓▓    ▓▓▓  ┃
┃  ▓  ▓▓ ▓   ▓▓       ▓▓    ▓▓▓▓ ┃    ┃     ▓▓▓▓   ▓▓      ▓▓▓    ▓▓▓▓ ┃
┃▓▓ ▓▓▓▓ ▓▓ ▓ ▓ ▓    ▓▓      ▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓   ▓▓      ▓▓▓     ▓▓▓ ┃
┃▓  ▓  ▓▓▓  ▓▓▓  ▓▓  ▓▓ ▓     ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓  ▓▓▓      ▓▓▓     ▓▓▓ ┃
┃ ▓▓ ▓  ▓  ▓▓     ▓ ▓ ▓▓▓▓▓ ▓▓▓ ▓┃    ┃ ▓▓       ▓▓        ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓     ▓ ▓▓    ▓▓ ▓▓    ▓▓ ▓▓  ┃    ┃ ▓▓       ▓▓        ▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓    ▓     ▓       ▓▓▓ ▓▓▓    ┃    ┃ ▓▓                  ▓▓▓▓▓▓▓    ┃
┃▓▓   ▓            ▓  ▓ ▓▓   ▓   ┃    ┃ ▓▓                   ▓▓▓       ┃
┃  ▓  ▓▓▓▓ ▓ ▓    ▓▓▓  ▓▓    ▓   ┃    ┃ ▓▓  ▓▓▓▓        ▓▓▓   ▓▓       ┃
┃▓▓▓  ▓ ▓▓   ▓   ▓▓▓▓   ▓▓▓▓  ▓▓▓┃    ┃     ▓▓▓▓        ▓▓▓   ▓▓       ┃
┃    ▓▓ ▓▓▓  ▓ ▓ ▓  ▓▓    ▓ ▓▓  ▓┃    ┃    ▓▓▓▓▓▓             ░░   ▓▓▓▓┃
┃▓▓  ▓ ▓▓▓▓▓ ▓▓  ▓   ▓ ▓▓▓   ▓▓ ▓┃    ┃    ▓▓▓▓▓▓▓            ░░   ▓▓▓▓┃
┃  ▓▓▓▓ ▓ ▓▓ ▓ ▓   ▓  ▓ ▓  ▓▓ ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓░            ░   ▓▓▓▓┃
┃ ▓▓ ▓▓▓ ▓▓ ▓   ▓  ▓▓ ▓  ▓▓   ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓        ▓▓▓  ▓▓▓    ▓┃
┃   ▓▓   ▓▓    ▓▓ ▓  ▓▓▓ ▓▓▓▓▓  ▓┃    ┃  ▓▓▓▓▓▓▓▓▓       ▓▓▓▓  ▓▓▓    ▓┃
┃▓▓▓▓ ▓▓▓▓▓▓      ▓▓▓▓         ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓        ▓▓┃
┃   ▓▓▓ ▓▓▓▓  ▓▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓   ▓▓▓▓▓▓ ┃
┃  ▓▓ ▓ ▓▓  ▓▓▓ ▓▓▓ ▓▓    ▓▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓░▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓ ┃
┃▓ ▓  ▓▓  ▓ ▓  ▓    ▓▓▓▓ ▓▓ ▓▓ ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓░░░▓▓▓▓▓▓ ┃
┃▓▓   ▓▓▓▓ ▓ ▓ ▓▓  ▓▓ ▓ ▓ ▓▓ ▓▓▓▓┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓    ▓▓▓░░░▓▓▓▓▓▓ ┃
┃▓▓▓ ▓ ▓▓▓▓▓▓ ▓  ▓ ▓    ▓    ▓ ▓ ┃    ┃▓▓░░░▓▓▓▓▓▓▓▓▓              ▓▓▓▓┃
┃▓  ▓▓  ▓▓ ▓▓▓ ▓         ▓   ▓▓▓▓┃    ┃▓▓░░░▓▓▓▓▓▓▓▓▓              ▓▓▓▓┃
┃ ▓▓ ▓ ▓ ▓▓▓ ▓▓▓▓ ▓ ▓ ▓▓   ▓  ▓▓▓┃    ┃   ░░▓▓▓▓▓▓▓▓▓      ▓▓      ▓▓▓▓┃
┃▓▓   ▓▓  ▓ ▓     ▓ ▓▓▓   ▓ ▓▓   ┃    ┃                    ▓▓          ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓   ▓▓ ▓ ▓▓   ▓  ▓▓▓ ▓▓ ▓  ▓▓  ┃    ┃     ▓▓  ▓▓▓      ▓▓        ▓▓  ┃
┃ ▓▓▓▓▓▓  ▓▓▓▓▓ ▓  ▓   ▓ ▓▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓       ▓▓▓  ┃
┃▓▓  ▓▓▓ ▓▓ ▓▓  ▓▓ ▓▓  ▓    ▓ ▓  ┃    ┃▓▓  ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓       ▓▓▓  ┃
┃▓     ▓▓▓▓▓    ▓▓ ▓▓▓▓▓  ▓▓▓ ▓▓▓┃    ┃▓▓    ▓▓▓▓▓▓   ▓▓▓▓▓▓░     ▓▓▓▓ ┃
┃▓▓     ▓ ▓▓ ▓   ▓▓▓▓      ▓  ▓ ▓┃    ┃       ▓▓▓▓▓   ▓▓▓▓▓       ▓▓▓▓ ┃
┃  ▓    ▓  ▓▓ ▓▓▓      ▓ ▓▓ ▓▓▓  ┃    ┃         ▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓ ┃
┃▓▓▓▓▓    ▓ ▓▓▓ ▓ ▓   ▓ ▓▓▓▓ ▓ ▓▓┃    ┃          ▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓ ┃
┃     ▓ ▓   ▓  ▓▓▓  ▓ ▓▓ ▓ ▓▓▓▓ ▓┃    ┃           ▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓ ┃
┃ ▓▓▓   ▓▓ ▓ ▓▓ ▓▓▓▓    ▓▓▓ ▓ ▓▓ ┃    ┃ ▓▓▓   ▓▓▓    ▓▓▓▓▓▓    ▓▓▓▓▓▓▓ ┃
┃▓▓▓▓▓ ▓ ▓▓    ▓   ▓▓▓    ▓▓ ▓▓▓▓┃    ┃ ▓▓▓   ▓▓▓    ▓▓  ▓▓▓   ▓▓▓▓▓▓▓ ┃
┃ ▓▓ ▓   ▓▓  ▓ ▓▓   ▓▓▓▓ ▓  ▓ ▓  ┃    ┃▓▓▓▓   ▓▓▓   ▓▓▓  ▓▓▓  ▓▓▓▓▓▓▓▓ ┃
┃▓▓▓  ▓▓▓  ▓ ▓▓▓ ▓ ▓ ▓  ▓▓▓▓▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓ ▓▓   ▓ ▓ ▓▓▓▓▓  ▓▓▓  ▓ ▓ ▓┃    ┃▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓  ░░░░ ┃
┃▓▓ ▓▓▓ ▓   ▓ ▓▓▓▓ ▓▓  ▓▓▓   ▓ ▓▓┃    ┃▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓  ▓▓▓  ░░░░ ┃
┃▓▓▓▓     ▓  ▓ ▓▓ ▓  ▓      ▓ ▓ ▓┃    ┃▓▓▓▓▓▓      ▓▓▓▓▓  ▓       ░▓▓▓▓┃
┃▓   ▓▓  ▓  ▓▓▓▓  ▓ ▓▓▓    ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓    ▓▓▓▓▓    ▓▓      ▓▓▓▓▓┃
┃▓ ▓▓▓▓  ▓▓ ▓▓▓  ▓  ▓  ▓▓   ▓  ▓ ┃    ┃  ▓▓▓▓   ▓▓▓▓▓▓    ▓▓      ▓▓▓▓ ┃
┃▓ ▓▓ ▓  ▓ ▓▓  ▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓▓▓ ┃    ┃  ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░▓▓▓▓▓▓ ┃
┃   ▓▓ ▓ ▓ ▓▓ ▓▓▓▓ ▓▓▓ ▓  ▓▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░▓▓▓▓▓▓ ┃
┃▓▓ ▓▓▓▓▓▓▓▓ ▓  ▓▓▓  ▓ ▓ ▓   ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓       ▓▓▓▓▓▓ ┃
┃ ▓▓▓▓▓▓▓ ▓     ▓ ▓  ▓▓   ▓▓▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓       ▓▓▓▓▓▓ ┃
┃▓▓  ▓▓  ▓ ▓▓▓ ▓▓▓▓▓ ▓ ▓▓ ▓▓▓▓▓  ┃    ┃▓▓▓▓▓▓    ▓▓▓  ▓▓▓       ▓▓▓▓▓  ┃
┃▓▓▓▓ ▓  ▓  ▓▓  ▓   ▓      ▓ ▓  ▓┃    ┃▓▓▓▓▓▓     ▓▓  ▓▓▓        ▓▓    ┃
┃▓▓ ▓ ▓  ▓▓ ▓▓▓ ▓ ▓▓  ▓ ▓  ▓     ┃    ┃▓▓▓▓▓▓     ▓▓ ░▓▓▓▓             ┃
┃  ▓ ▓▓▓▓▓     ▓ ▓▓     ▓     ▓▓ ┃    ┃  ▓▓▓▓░        ▓▓▓▓             ┃
┃ ▓  ▓      ▓ ▓    ▓  ▓▓▓▓ ▓ ▓ ▓ ┃    ┃                ▓▓▓  ▓▓     ▓▓▓ ┃
┃▓▓▓ ▓       ▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓┃    ┃                ▓▓▓▓▓▓▓   ▓▓▓▓▓▓┃
┃        ▓   ▓   ▓ ▓  ▓   ▓▓▓▓ ▓▓┃    ┃               ▓▓▓▓  ▓▓   ▓▓▓▓▓▓┃
┃▓ ▓▓▓  ▓  ▓ ▓▓▓▓▓ ▓  ▓▓▓  ▓ ▓▓  ┃    ┃  ▓▓        ▓▓▓▓▓▓▓  ▓▓▓  ▓▓▓▓▓ ┃
┃  ▓▓  ▓     ▓▓ ▓▓▓▓▓   ▓▓  ▓▓ ▓▓┃    ┃  ▓▓        ▓▓▓▓▓▓▓   ▓▓   ▓▓▓▓ ┃
┃▓▓▓      ▓  ▓   ▓▓    ▓   ▓ ▓▓▓ ┃    ┃▓▓▓            ▓▓▓▓         ▓▓▓ ┃
┃▓▓▓ ▓▓     ▓▓ ▓▓ ▓▓▓ ▓▓▓    ▓ ▓ ┃    ┃▓▓▓             ▓▓▓             ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓ ▓  ▓▓ ▓ ▓     ▓   ▓  ▓  ▓▓ ┃    ┃         ▓▓▓                 ▓▓ ┃
┃▓   ▓▓▓  ▓▓▓▓  ▓ ▓   ▓▓▓▓▓ ▓ ▓▓ ┃    ┃     ▓▓  ▓▓▓          ▓▓▓░░░░▓▓ ┃
┃  ▓   ▓  ▓▓   ▓     ▓ ▓▓▓ ▓ ▓▓  ┃    ┃     ▓▓  ▓▓▓          ▓▓▓░░░░▓▓ ┃
┃ ▓ ▓ ▓▓    ▓ ▓▓ ▓ ▓▓    ▓ ▓▓ ▓▓▓┃    ┃                    ▓▓▓▓▓    ▓▓▓┃
┃  ▓▓   ▓ ▓▓ ▓  ▓  ▓ ▓▓▓▓      ▓▓┃    ┃ ▓▓▓              ▓▓▓▓▓▓▓     ▓▓┃
┃▓▓▓▓ ▓  ▓   ▓     ▓▓  ▓▓▓▓ ▓   ▓┃    ┃ ▓▓▓              ▓▓▓▓▓▓▓▓    ▓▓┃
┃    ▓ ▓  ▓▓ ▓ ▓▓▓  ▓ ▓▓▓▓▓ ▓ ▓▓▓┃    ┃                   ▓▓▓▓▓▓▓▓▓░░▓▓┃
┃▓ ▓   ▓   ▓      ▓  ▓▓▓▓ ▓▓▓ ▓ ▓┃    ┃                    ▓▓▓▓▓▓▓▓░░▓▓┃
┃  ▓ ▓▓         ▓ ▓ ▓▓▓▓▓▓  ▓▓ ▓▓┃    ┃                    ▓▓▓▓▓▓▓▓░░░ ┃
┃▓▓ ▓  ▓▓▓ ▓▓ ▓▓       ▓▓ ▓▓▓ ▓ ▓┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓▓░░░ ┃
┃  ▓   ▓  ▓ ▓  ▓  ▓▓  ▓▓ ▓ ▓▓ ▓  ┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓▓░░░ ┃
┃▓▓    ▓▓▓▓▓ ▓▓    ▓   ▓   ▓  ▓▓▓┃    ┃      ▓▓▓▓                   ▓▓▓┃
┃▓      ▓▓▓  ▓   ▓▓   ▓▓  ▓   ▓▓▓┃    ┃      ▓▓▓▓      ▓▓           ▓▓▓┃
┃    ▓▓▓    ▓ ▓ ▓▓▓ ▓   ▓▓▓ ▓  ▓▓┃    ┃                ▓▓▓     ▓▓   ▓▓▓┃
┃ ▓ ▓ ▓  ▓ ▓       ▓▓ ▓  ▓ ▓  ▓ ▓┃    ┃                 ▓▓▓    ▓▓▓  ▓▓▓┃
┃▓▓▓▓ ▓ ▓▓▓▓ ▓   ▓▓▓▓▓ ▓ ▓ ▓ ▓  ▓┃    ┃▓▓▓▓     ▓▓      ▓▓▓    ▓▓▓     ┃
┃▓▓▓   ▓ ▓ ▓      ▓▓     ▓▓▓ ▓▓  ┃    ┃▓▓▓▓     ▓▓      ▓▓▓    ▓▓▓     ┃
┃ ▓▓ ▓     ▓▓ ▓▓ ▓ ▓▓  ▓▓▓▓ ▓  ▓ ┃    ┃▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓     ┃
┃▓▓▓▓▓▓ ▓▓  ▓▓▓ ▓▓▓▓  ▓ ▓ ▓▓    ▓┃    ┃▓▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓      ┃
┃ ▓ ▓▓▓ ▓▓ ▓ ▓ ▓▓▓  ▓▓▓ ▓       ▓┃    ┃ ▓▓▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓▓▓▓▓      ┃
┃▓ ▓▓▓▓▓▓  ▓  ▓▓▓   ▓ ▓▓ ▓▓▓  ▓  ┃    ┃  ▓▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓▓▓▓▓     ┃
┃   ▓▓▓ ▓▓▓ ▓▓▓    ▓ ▓▓▓ ▓▓▓▓▓ ▓▓┃    ┃   ▓▓▓▓▓▓   ▓▓     ▓▓▓▓▓▓▓▓  ▓▓ ┃
┃   ▓  ▓▓  ▓ ▓▓     ▓▓ ▓▓ ▓   ▓▓ ┃    ┃      ▓▓    ▓▓     ▓▓▓▓▓▓▓▓  ▓▓ ┃
┃▓▓    ▓       ▓▓▓  ▓   ▓ ▓▓  ▓  ┃    ┃▓▓    ▓     ▓▓▓▓             ▓▓ ┃
┃▓▓▓  ▓▓    ▓▓▓▓▓ ▓▓▓ ▓   ▓ ▓▓▓▓ ┃    ┃▓▓   ▓▓     ▓▓▓▓                ┃
┃ ▓  ▓▓▓  ▓▓ ▓▓▓    ▓  ▓        ▓┃    ┃▓▓   ▓▓     ▓▓▓▓                ┃
┃▓▓ ▓           ▓ ▓   ▓▓  ▓ ▓▓▓ ▓┃    ┃▓▓          ▓▓▓                 ┃
┃▓  ▓▓ ▓▓▓ ▓▓▓ ▓    ▓▓ ▓ ▓▓▓ ▓ ▓ ┃    ┃▓▓▓     ▓▓▓▓▓▓▓    ▓▓  ▓▓▓░░    ┃
┃▓▓▓▓   ▓ ▓▓▓ ▓▓ ▓▓ ▓▓  ▓▓  ▓ ▓  ┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓░     ┃
┃ ▓   ▓ ▓▓▓ ▓▓  ▓▓ ▓  ▓ ▓▓▓ ▓▓   ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓      ┃
┃▓  ▓  ▓▓    ▓▓ ▓ ▓      ▓  ▓ ▓  ┃    ┃      ▓▓    ▓▓                  ┃
┃▓    ▓▓   ▓ ▓▓   ▓▓   ▓  ▓▓▓ ▓  ┃    ┃            ▓▓                  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓ ▓ ▓  ▓  ▓▓▓▓▓ ▓ ▓▓▓▓▓▓  ▓▓▓▓┃    ┃ ▓▓         ▓▓▓     ▓▓▓▓▓▓  ▓▓▓▓┃
┃  ▓▓  ▓ ▓   ▓▓ ▓    ▓ ▓▓▓▓ ▓▓▓ ▓┃    ┃ ▓▓         ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓  ▓ ▓  ▓ ▓▓ ▓ ▓▓  ▓▓  ▓ ▓▓ ▓ ▓┃    ┃   ░     ▓▓▓▓▓▓▓▓   ▓   ▓▓▓▓▓  ▓┃
┃   ▓ ▓ ▓▓▓▓▓  ▓ ▓  ▓   ▓ ▓ ▓   ▓┃    ┃   ░░▓▓▓▓▓▓▓▓▓▓▓▓   ▓     ░░   ▓┃
┃▓▓▓▓  ▓▓▓ ▓ ▓▓▓▓ ▓ ▓▓▓  ▓   ▓▓▓▓┃    ┃▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓    ░░   ▓┃
┃▓▓▓  ▓▓▓ ▓        ▓▓▓▓▓ ▓▓▓▓   ▓┃    ┃▓▓▓  ▓▓▓▓▓         ▓▓▓    ▓▓   ▓┃
┃ ▓▓  ▓▓ ▓▓ ▓    ▓  ▓ ▓    ▓▓ ▓ ▓┃    ┃ ▓▓  ▓▓▓▓▓         ▓▓▓    ▓▓   ▓┃
┃  ▓ ▓▓  ▓▓ ▓▓ ▓   ▓▓ ▓ ▓   ▓ ▓ ▓┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓             ▓▓▓▓▓▓┃
┃ ▓▓ ▓▓  ▓ ▓▓ ▓▓ ▓▓   ▓ ▓▓ ▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓▓▓ ▓▓        ▓▓▓▓▓▓┃
┃▓▓ ▓▓▓  ▓ ▓▓ ▓  ▓▓       ▓  ▓  ▓┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓▓▓ ▓▓           ░  ┃
┃ ▓ ▓▓▓▓ ▓▓ ▓▓▓▓▓    ▓▓   ▓ ▓ ▓▓▓┃    ┃ ▓▓▓▓▓   ▓▓▓▓▓▓                 ┃
┃▓ ▓ ▓   ▓        ▓▓  ▓▓ ▓ ▓▓    ┃    ┃                                ┃
┃ ▓   ▓▓  ▓ ▓▓▓    ▓ ▓▓ ▓     ▓▓▓┃    ┃           ▓▓▓       ▓▓▓     ▓▓ ┃
┃ ▓ ▓  ▓    ▓▓▓  ▓ ▓   ▓ ▓  ▓▓▓ ▓┃    ┃           ▓▓▓       ▓▓▓▓    ▓▓ ┃
┃▓    ▓▓▓  ▓▓▓ ▓▓▓  ▓ ▓▓ ▓▓      ┃    ┃           ▓▓▓      ▓▓▓▓▓▓      ┃
┃  ▓▓    ▓▓   ▓    ▓ ▓▓▓ ▓▓▓▓  ▓▓┃    ┃  ▓▓       ▓▓▓      ▓▓▓▓▓▓▓     ┃
┃▓▓▓▓▓ ▓  ▓ ▓▓▓ ▓    ▓   ▓▓      ┃    ┃ ▓▓▓▓      ▓▓▓      ▓▓  ▓▓▓     ┃
┃ ▓▓▓ ▓▓▓ ▓▓ ▓ ▓▓▓▓ ▓▓▓  ▓ ▓ ▓▓▓ ┃    ┃ ▓▓▓▓▓▓     ▓▓      ▓▓  ▓▓  ▓▓▓ ┃
┃▓  ▓ ▓ ▓    ▓   ▓ ▓  ▓▓▓▓   ▓▓▓▓┃    ┃  ▓▓▓▓▓▓            ▓▓▓▓▓   ▓▓▓ ┃
┃  ▓▓▓▓▓ ▓▓ ▓ ▓   ▓▓ ▓ ▓ ▓       ┃    ┃  ▓▓▓▓▓▓         ▓▓▓░░░░░       ┃
┃  ▓▓  ▓▓  ▓▓▓▓   ▓▓▓   ▓  ▓▓  ▓ ┃    ┃  ▓▓▓▓▓▓▓░░▓▓▓   ▓▓▓▓░░░▓▓▓▓    ┃
┃▓▓ ▓▓ ▓▓▓▓ ▓▓▓   ▓  ▓ ▓ ▓ ▓▓▓▓ ▓┃    ┃▓▓▓▓  ▓▓▓░░▓▓▓   ▓▓▓▓░░░▓▓▓▓▓▓  ┃
┃▓▓▓▓  ▓▓    ▓ ▓ ▓▓▓ ▓▓  ▓▓ ▓ ▓ ▓┃    ┃▓▓▓▓  ▓▓  ░▓▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓  ┃
┃       ▓ ▓ ▓▓▓▓▓▓▓▓▓▓ ▓   ▓▓▓ ▓ ┃    ┃      ▓▓  ▓▓▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓  ┃
┃ ▓   ▓▓▓ ▓▓ ▓    ▓▓▓ ▓▓▓▓▓▓▓▓  ▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓░░░▓▓▓▓▓▓  ┃
┃▓▓ ▓▓▓  ▓▓  ▓▓▓  ▓▓▓    ▓▓ ▓▓ ▓▓┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓▓   ▓▓▓    ▓▓▓▓▓   ┃
┃ ▓▓ ▓▓   ▓▓   ▓ ▓  ▓    ▓▓▓▓▓   ┃    ┃ ▓▓▓▓▓  ▓▓▓      ▓▓▓    ▓▓▓▓▓   ┃
┃ ▓▓  ▓ ▓▓▓ ▓    ▓ ▓   ▓    ▓    ┃    ┃ ▓▓   ░▓▓▓▓     ▓▓▓▓      ▓▓    ┃
┃▓  ▓  ▓▓▓▓▓▓▓▓  ▓▓▓▓▓     ▓▓  ▓▓┃    ┃ ▓▓    ▓▓▓▓▓▓▓  ▓▓▓▓▓           ┃
┃▓ ▓  ▓  ▓▓▓▓ ▓▓▓  ▓ ▓▓▓▓▓      ▓┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓           ┃
┃▓▓▓ ▓▓▓  ▓ ▓ ▓ ▓ ▓▓         ▓▓▓ ┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓          ▓▓ ┃
┃▓▓▓   ▓ ▓▓ ▓ ▓▓▓▓▓ ▓ ▓▓▓    ▓ ▓▓┃    ┃▓▓▓          ▓▓▓▓▓▓          ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓  ▓▓▓▓ ▓      ▓▓ ▓  ▓▓▓  ▓   ▓┃    ┃     ▓▓         ▓▓     ▓▓       ┃
┃ ▓ ▓ ▓▓   ▓ ▓▓  ▓▓   ▓ ▓▓▓▓ ▓▓ ▓┃    ┃  ▓▓▓▓▓   ▓▓▓▓  ▓▓    ▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓▓    ▓▓▓▓▓     ▓▓▓▓ ▓▓▓▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓   ▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓ ▓▓ ▓▓▓ ▓  ▓  ▓▓▓▓▓▓▓▓    ▓▓  ┃    ┃ ▓▓▓▓▓▓▓  ▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓   ▓▓   ▓  ▓▓  ▓▓    ▓▓▓▓▓  ▓▓┃    ┃ ▓▓  ▓▓▓  ▓      ▓▓    ▓▓▓    ▓▓┃
┃ ▓▓  ▓ ▓ ▓▓   ▓   ▓  ▓  ▓▓    ▓▓┃    ┃ ▓▓    ▓▓▓▓      ▓▓     ▓▓    ▓▓┃
┃▓▓▓▓   ▓▓ ▓▓▓  ▓ ▓▓   ▓  ▓    ▓ ┃    ┃▓▓▓    ▓▓▓▓     ▓▓▓             ┃
┃▓ ▓   ▓ ▓      ▓▓▓ ▓ ▓▓    ▓   ▓┃    ┃▓▓▓             ▓▓▓             ┃
┃▓ ▓       ▓▓ ▓   ▓▓ ▓ ▓▓ ▓▓▓▓▓  ┃    ┃▓▓▓       ▓▓▓   ▓▓▓▓░▓▓▓░░▓▓▓   ┃
┃▓ ▓▓ ▓ ▓ ▓▓▓▓ ▓▓ ▓▓▓ ▓ ▓ ▓ ▓  ▓▓┃    ┃▓▓▓▓      ▓▓▓▓  ▓▓▓▓▓▓▓▓░░▓▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓  ▓ ▓▓  ▓▓   ▓▓▓▓ ▓▓▓▓▓ ┃    ┃▓▓▓▓ ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓ ┃
┃  ▓▓ ▓▓▓▓  ▓ ▓▓▓ ▓▓▓ ▓▓  ▓   ▓ ▓┃    ┃  ▓▓ ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓ ┃
┃  ▓  ▓ ▓▓▓   ▓▓▓ ▓ ▓ ▓   ▓ ▓▓▓  ┃    ┃      ▓▓▓▓   ▓▓▓▓▓▓▓▓▓    ▓▓▓▓  ┃
┃   ▓   ▓ ▓▓▓ ▓▓ ▓  ▓ ▓ ▓ ▓ ▓    ┃    ┃        ▓▓▓  ▓▓▓▓▓▓▓▓░   ▓▓▓▓   ┃
┃▓▓       ▓     ▓▓▓▓▓▓    ▓▓▓▓   ┃    ┃▓▓      ▓▓▓     ▓▓▓▓░░   ▓▓▓▓   ┃
┃▓▓▓▓▓  ▓▓▓▓▓    ▓ ▓▓ ▓ ▓  ▓▓▓▓ ▓┃    ┃▓▓▓▓    ▓▓▓     ▓▓▓▓░░   ▓▓▓▓   ┃
┃▓▓  ▓   ▓▓  ▓▓▓ ▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓▓┃    ┃▓▓▓▓    ▓▓▓    ▓▓▓▓▓░▓▓▓▓▓▓▓▓   ┃
┃  ▓▓   ▓  ▓ ▓  ▓▓▓    ▓ ▓  ▓▓   ┃    ┃ ▓▓            ▓▓    ▓▓▓▓▓▓▓▓   ┃
┃ ▓▓   ▓    ▓   ▓   ▓ ▓ ▓▓▓▓   ▓▓┃    ┃ ▓▓                  ▓▓▓▓▓▓▓    ┃
┃▓ ▓ ▓ ▓  ▓▓     ▓ ▓ ▓▓▓▓▓▓▓▓▓   ┃    ┃ ▓▓                ▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓  ▓  ▓    ▓    ▓▓▓ ▓▓   ▓ ▓ ▓┃    ┃ ▓▓                ▓▓▓▓▓   ▓    ┃
┃   ▓▓▓   ▓        ▓ ▓▓▓  ▓ ▓    ┃    ┃    ▓▓            ▓▓▓▓▓▓   ▓    ┃
┃▓   ▓    ▓ ▓▓▓ ▓▓▓  ▓  ▓ ▓ ▓▓ ▓ ┃    ┃   ▓▓▓     ▓▓▓  ▓▓▓▓▓    ▓▓▓    ┃
┃  ▓▓▓▓ ▓   ▓▓▓   ▓▓▓▓  ▓ ▓▓ ▓ ▓▓┃    ┃  ▓▓▓▓     ▓▓▓  ▓▓▓▓▓    ▓▓▓▓   ┃
┃  ▓▓▓▓ ▓▓▓▓▓  ▓ ▓   ▓▓    ▓▓    ┃    ┃  ▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓   ┃
┃▓▓      ▓ ▓▓ ▓▓▓▓▓▓  ▓▓  ▓▓ ▓▓  ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ▓▓▓▓▓  ┃
┃      ▓▓▓▓▓ ▓▓ ▓▓▓ ▓  ▓▓▓ ▓▓▓▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓  ┃
┃  ▓▓  ▓ ▓▓ ▓  ▓ ▓      ▓ ▓   ▓  ┃    ┃       ▓▓▓▓  ▓▓▓▓      ▓▓▓▓     ┃
┃▓  ▓▓   ▓▓▓  ▓ ▓▓  ▓▓  ▓ ▓ ▓    ┃    ┃  ▓▓▓  ▓▓▓▓            ▓▓▓▓     ┃
┃  ▓▓▓▓▓▓▓▓▓ ▓ ▓     ▓▓▓▓▓▓▓▓▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓░       ▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓  ▓▓ ▓▓ ▓▓ ▓▓  ▓▓ ▓ ▓  ▓ ▓  ▓┃    ┃  ▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓   ▓▓▓  ┃
┃ ▓▓▓ ▓    ▓ ▓      ▓ ▓▓▓    ▓▓▓ ┃    ┃                     ▓▓▓    ▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓  ▓ ▓ ▓▓ ▓▓    ▓▓▓▓▓ ▓▓  ▓▓▓ ┃    ┃        ▓▓▓▓      ▓▓▓▓      ▓▓  ┃
┃ ▓    ▓ ▓ ▓▓  ▓ ▓▓▓    ▓ ▓  ▓▓  ┃    ┃       ▓▓▓▓▓▓   ▓▓▓▓▓▓░     ▓▓▓ ┃
┃ ▓ ▓  ▓▓ ▓▓▓▓▓  ▓▓▓▓ ▓▓ ▓  ▓▓▓▓▓┃    ┃      ▓▓▓▓▓▓▓   ▓▓▓▓▓▓      ▓▓▓ ┃
┃▓ ▓  ▓ ▓▓▓        ▓ ▓▓   ▓   ▓  ┃    ┃      ▓▓▓▓▓▓▓       ▓▓       ▓▓ ┃
┃    ▓▓  ▓ ▓▓▓▓   ▓    ▓ ▓    ▓▓▓┃    ┃        ▓▓▓▓▓▓               ▓▓ ┃
┃     ▓  ▓ ▓▓ ▓▓▓   ▓      ▓ ▓   ┃    ┃          ▓▓▓▓▓▓             ▓  ┃
┃  ▓▓      ▓▓ ▓▓▓▓▓ ▓▓    ▓▓ ▓▓  ┃    ┃          ▓▓▓▓▓▓▓▓▓▓       ▓▓▓  ┃
┃▓ ▓ ▓ ▓   ▓ ▓   ▓▓▓▓  ▓▓▓  ▓▓▓▓ ┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░ ▓▓▓▓ ┃
┃  ▓ ▓ ▓▓  ▓▓▓ ▓▓  ▓▓▓▓▓▓ ▓ ▓  ▓▓┃    ┃          ▓▓▓▓▓   ▓▓▓▓▓▓░     ▓▓┃
┃▓ ▓ ▓    ▓   ▓▓   ▓ ▓▓ ▓  ▓▓  ▓▓┃    ┃           ▓▓▓▓   ▓▓▓▓▓▓      ▓▓┃
┃  ▓   ▓  ▓ ▓▓▓▓  ▓▓▓  ▓ ▓   ▓ ▓▓┃    ┃           ▓▓▓▓  ▓▓  ▓▓▓      ▓▓┃
┃ ▓▓▓▓    ▓ ▓   ▓▓▓   ▓ ▓ ▓▓  ▓▓▓┃    ┃           ▓  ▓▓▓▓   ▓▓▓▓▓    ▓▓┃
┃  ▓   ▓ ▓  ▓  ▓▓     ▓▓▓▓▓  ▓ ▓▓┃    ┃           ░  ▓▓▓    ▓▓▓▓▓    ▓▓┃
┃ ▓ ▓▓▓▓▓ ▓▓▓  ▓▓▓  ▓ ▓▓▓   ▓ ▓▓ ┃    ┃  ▓▓▓▓    ░   ▓▓     ▓▓▓      ▓▓┃
┃▓   ▓      ▓▓    ▓  ▓▓ ▓  ▓▓   ▓┃    ┃  ▓▓▓▓              ▓▓▓▓        ┃
┃▓▓ ▓▓▓      ▓  ▓  ▓  ▓▓  ▓    ▓ ┃    ┃▓▓▓▓▓▓              ▓▓▓▓        ┃
┃▓▓ ▓▓▓ ▓  ▓    ▓▓▓▓▓▓ ▓▓ ▓▓ ▓   ┃    ┃▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃ ▓ ▓ ▓ ▓    ▓▓▓▓ ▓ ▓▓▓▓▓▓▓ ▓▓  ▓┃    ┃   ▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃   ▓  ▓▓▓▓ ▓ ▓   ▓▓ ▓  ▓ ▓▓ ▓▓▓ ┃    ┃   ░░░░▓▓▓▓     ▓▓▓▓    ▓▓▓▓▓   ┃
┃▓▓ ▓ ▓  ▓▓▓▓ ▓ ▓▓    ▓  ▓▓▓▓ ▓ ▓┃    ┃   ░░░░▓▓▓▓▓    ▓▓      ▓▓▓▓▓   ┃
┃▓ ▓ ▓▓ ▓   ▓    ▓▓▓▓ ▓▓ ▓  ▓    ┃    ┃   ░░░░▓▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓▓   ┃
┃  ▓  ▓  ▓▓▓ ▓ ▓▓▓▓    ▓▓▓▓ ▓▓   ┃    ┃ ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓▓ ▓▓ ▓▓▓▓▓ ▓  ▓▓ ▓▓ ▓  ▓▓  ┃    ┃▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓      ▓▓▓   ▓▓  ┃
┃▓▓   ▓  ▓ ▓▓▓▓       ▓  ▓   ▓▓ ▓┃    ┃▓▓▓▓▓▓    ▓▓▓▓▓       ░░    ▓▓▓ ┃
┃▓▓ ▓▓▓       ▓▓  ▓▓ ▓ ▓ ▓    ▓▓▓┃    ┃▓▓▓▓▓▓       ▓▓  ▓▓▓░░░░     ▓▓ ┃
┃  ▓ ▓▓ ▓▓▓ ▓ ▓▓▓ ▓▓▓ ▓▓▓ ▓▓▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓░░░░        ┃
┃▓ ▓ ▓ ▓▓▓ ▓  ▓▓▓▓▓ ▓  ▓ ▓   ▓  ▓┃    ┃  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓   ░        ┃
┃▓ ▓▓▓▓  ▓▓▓   ▓▓▓  ▓▓  ▓ ▓▓▓ ▓▓ ┃    ┃  ▓▓▓▓  ▓▓   ▓▓▓▓▓▓▓    ░   ▓▓▓ ┃
┃  ▓▓ ▓  ▓    ▓▓ ▓ ▓  ▓ ▓     ▓▓ ┃    ┃  ▓▓▓▓        ▓▓▓▓▓▓▓       ▓▓▓ ┃
┃    ▓▓ ▓▓  ▓     ▓ ▓▓  ▓▓▓ ▓▓▓ ▓┃    ┃  ▓▓▓              ▓▓▓▓▓    ▓▓▓ ┃
┃  ▓▓    ▓▓ ▓ ▓  ▓▓▓ ▓▓▓    ▓ ▓▓ ┃    ┃  ▓▓               ▓▓▓▓▓    ▓▓  ┃
┃▓▓▓▓ ▓      ▓▓      ▓ ▓▓▓ ▓  ▓  ┃    ┃  ▓▓                 ▓▓▓        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓   ▓  ▓   ▓▓    ▓ ▓▓▓▓▓     ▓┃    ┃                                ┃
┃ ▓ ▓ ▓ ▓  ▓ ▓ ▓▓▓▓▓ ▓ ▓        ▓┃    ┃              ▓▓▓▓▓░            ┃
┃  ▓▓▓▓  ▓ ▓  ▓▓▓ ▓▓▓ ▓    ▓▓▓▓▓▓┃    ┃  ▓▓▓         ▓▓▓▓▓░░     ▓▓▓▓▓ ┃
┃▓▓  ▓  ▓▓   ▓ ▓▓▓▓  ▓▓ ▓▓ ▓ ▓▓  ┃    ┃ ▓▓▓▓  ▓▓     ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓▓  ▓▓▓ ▓▓   ▓▓   ▓▓▓▓ ▓▓▓▓▓ ┃    ┃▓▓▓▓▓  ▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓▓▓▓  ┃
┃▓ ▓▓  ▓▓▓▓▓▓▓▓ ▓▓▓   ▓ ▓▓▓     ▓┃    ┃▓▓▓▓▓  ▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓     ┃
┃▓▓  ▓  ▓ ▓  ▓  ▓▓  ▓▓▓▓▓ ▓▓▓ ▓  ┃    ┃▓▓     ▓▓▓▓▓▓░░▓▓    ▓▓▓▓▓▓     ┃
┃▓▓   ▓▓ ▓▓▓  ▓ ▓▓     ▓▓    ▓ ▓▓┃    ┃▓▓      ▓▓▓▓▓░░▓▓   ▓▓▓▓▓▓      ┃
┃▓ ▓▓ ▓ ▓   ▓▓ ▓▓   ▓▓▓ ▓▓▓  ▓▓ ▓┃    ┃▓▓▓▓      ▓▓░░░▓▓   ▓▓▓▓▓▓      ┃
┃▓▓ ▓▓  ▓ ▓▓▓    ▓    ▓▓▓▓▓   ▓▓ ┃    ┃ ▓▓▓      ▓▓░░      ▓▓▓▓▓▓   ░  ┃
┃▓  ▓ ▓  ▓   ▓▓      ▓▓ ▓▓▓▓▓   ▓┃    ┃   ░░     ░░░░      ▓▓▓▓▓▓▓  ░░ ┃
┃ ▓▓ ▓▓▓▓▓ ▓▓ ▓ ▓    ▓ ▓▓▓▓  ▓▓▓▓┃    ┃   ░░▓▓▓▓▓░░░▓▓       ▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓ ▓▓▓▓▓  ▓▓▓▓ ▓   ▓    ▓▓ ▓▓▓┃    ┃    ░▓▓▓▓▓░░░▓▓           ▓▓▓▓▓▓┃
┃▓  ▓ ▓▓  ▓ ▓ ▓    ▓      ▓ ▓  ▓▓┃    ┃     ▓▓▓▓▓░░░░               ▓▓▓┃
┃▓  ▓  ▓▓  ▓   ▓ ▓   ▓▓▓▓     ▓ ▓┃    ┃           ░░░        ▓▓     ▓▓▓┃
┃▓▓▓▓▓    ▓▓▓▓ ▓ ▓ ▓▓ ▓ ▓  ▓  ▓▓▓┃    ┃▓▓▓▓       ▓▓▓▓▓▓     ▓▓     ▓▓▓┃
┃▓     ▓     ▓▓▓▓▓   ▓  ▓▓   ▓▓ ▓┃    ┃▓▓▓▓       ▓▓▓▓▓▓    ▓▓▓▓    ▓▓▓┃
┃▓▓▓▓▓▓  ▓▓▓ ▓▓ ▓▓▓▓  ▓▓ ▓▓▓▓ ▓ ▓┃    ┃▓▓▓▓▓      ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓▓ ▓  ▓ ▓ ▓▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓▓ ▓┃    ┃▓▓▓▓▓       ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓  ┃
┃▓▓ ▓       ▓  ▓  ▓▓  ▓▓▓▓   ▓   ┃    ┃▓▓▓▓        ▓▓▓     ░▓▓▓▓▓  ░░  ┃
┃ ▓▓ ▓▓  ▓▓▓  ▓▓     ▓▓▓▓ ▓ ▓ ▓▓ ┃    ┃▓▓▓      ▓▓▓▓▓▓     ░▓▓▓▓▓  ░░  ┃
┃▓▓ ▓     ▓▓▓▓▓  ▓▓ ▓ ▓   ▓  ▓  ▓┃    ┃▓▓       ▓▓▓▓▓      ░▓▓▓▓▓▓▓░░  ┃
┃▓▓     ▓ ▓▓    ▓ ▓▓ ▓▓ ▓ ▓ ▓ ▓  ┃    ┃▓▓       ▓▓▓       ░░▓▓▓▓▓▓▓▓▓  ┃
┃     ▓   ▓ ▓    ▓▓   ▓▓ ▓▓▓▓ ▓▓ ┃    ┃         ░░░    ▓▓▓  ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓   ▓▓▓▓  ▓▓   ▓ ▓ ▓  ▓▓▓   ▓ ▓▓┃    ┃    ▓▓▓▓ ░░░   ▓▓▓▓   ▓▓▓▓   ▓▓ ┃
┃ ▓▓ ▓▓▓▓ ▓ ▓▓▓  ▓▓▓▓  ▓  ▓    ▓ ┃    ┃    ▓▓▓▓ ░▓▓▓  ▓▓▓▓             ┃
┃  ▓   ▓  ▓▓ ▓ ▓▓▓  ▓ ▓   ▓  ▓  ▓┃    ┃    ▓▓▓▓░▓▓▓▓  ▓▓▓              ┃
┃▓▓  ▓▓▓ ▓   ▓▓   ▓    ▓ ▓    ▓ ▓┃    ┃    ▓▓▓▓▓▓▓▓▓                   ┃
┃    ▓▓ ▓ ▓▓▓    ▓   ▓▓ ▓▓ ▓ ▓   ┃    ┃    ▓▓▓▓▓▓▓▓▓       ▓▓          ┃
┃▓     ▓  ▓▓▓▓▓      ▓▓    ▓▓▓▓ ▓┃    ┃    ▓▓  ▓▓▓▓▓▓      ▓▓          ┃
┃ ▓ ▓▓▓  ▓▓  ▓▓ ▓ ▓   ▓▓  ▓   ▓  ┃    ┃    ▓▓  ▓▓▓▓▓▓                  ┃
┃  ▓ ▓▓ ▓▓▓▓  ▓▓ ▓ ▓▓   ▓   ▓ ▓  ┃    ┃    ▓▓  ▓▓                      ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓▓▓▓ ▓ ▓▓  ▓ ▓▓▓ ▓   ▓ ▓ ▓ ┃    ┃   ▓▓                           ┃
┃▓▓ ▓▓      ▓ ▓▓      ▓  ▓▓▓▓▓   ┃    ┃ ▓▓▓▓                   ▓▓      ┃
┃ ▓▓ ▓   ▓    ▓  ▓▓▓▓   ▓▓ ▓    ▓┃    ┃ ▓▓▓▓            ▓▓▓    ▓▓      ┃
┃▓ ▓ ▓   ▓  ▓   ▓  ▓▓▓▓       ▓ ▓┃    ┃ ░░░░           ▓▓▓▓▓▓          ┃
┃▓  ▓ ▓▓▓▓▓▓ ▓ ▓▓▓▓ ▓▓▓▓▓ ▓  ▓ ▓ ┃    ┃ ░░░░   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃ ▓▓▓▓   ▓ ▓▓▓▓▓▓▓  ▓ ▓▓▓▓ ▓▓▓  ▓┃    ┃ ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓  ▓  ▓ ▓▓ ▓▓▓   ▓▓    ▓▓ ▓▓▓ ▓┃    ┃ ▓▓▓▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃ ▓▓▓ ▓▓ ▓▓▓  ▓    ▓▓▓▓ ▓ ▓    ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓  ▓    ▓▓▓   ░░      ┃
┃ ▓   ▓▓▓▓    ▓  ▓▓ ▓  ▓ ▓  ▓ ▓▓▓┃    ┃     ▓▓▓▓▓   ▓  ▓▓▓▓    ░░   ▓▓▓┃
┃▓▓  ▓  ▓▓▓ ▓▓▓  ▓▓  ▓  ▓▓▓   ▓▓▓┃    ┃     ▓▓▓▓▓ ▓▓▓  ▓▓▓▓    ░░   ▓▓▓┃
┃▓ ▓  ▓▓▓▓▓ ▓▓▓  ▓▓▓  ▓  ▓ ▓▓▓▓▓▓┃    ┃    ▓▓▓▓▓▓ ▓▓▓  ▓▓▓▓    ▓▓▓▓▓▓▓▓┃
┃  ▓ ▓▓▓▓▓▓  ▓ ▓ ▓ ▓▓▓▓▓  ▓▓ ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓▓ ▓   ▓▓  ▓▓▓▓  ▓ ▓▓▓▓  ▓▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓▓ ▓▓▓▓  ▓  ▓▓▓▓  ▓▓ ▓ ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓ ▓▓▓ ▓▓  ▓ ▓   ▓▓  ▓ ▓  ▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓    ▓  ▓▓  ▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓    ▓▓ ▓▓ ▓▓▓ ▓▓▓▓  ▓▓▓  ▓┃    ┃ ▓▓▓▓▓       ▓▓  ▓▓░░▓▓▓  ▓▓  ▓▓┃
┃▓▓ ▓    ▓    ▓   ▓▓▓ ▓  ▓ ▓   ▓▓┃    ┃ ▓▓         ▓▓▓  ▓▓░░▓▓   ▓▓  ▓▓┃
┃     ▓  ▓ ▓▓ ▓▓ ▓ ▓  ▓▓   ▓▓▓ ▓ ┃    ┃            ▓▓   ▓▓  ▓▓   ▓▓░░░ ┃
┃▓    ▓▓ ▓▓  ▓▓  ▓▓    ▓▓  ▓  ▓  ┃    ┃     ▓▓░░░░░▓▓   ▓▓   ▓▓  ▓▓░░░ ┃
┃▓  ▓ ▓▓   ▓ ▓▓   ▓▓ ▓ ▓▓▓▓▓ ▓▓▓ ┃    ┃     ▓▓░░░░░▓▓   ▓▓   ▓▓▓▓▓  ▓▓ ┃
┃▓▓▓ ▓▓ ▓▓▓ ▓ ▓ ▓ ▓ ▓  ▓ ▓ ▓  ▓▓ ┃    ┃   ░ ▓▓░░░░░▓▓   ▓▓   ▓▓▓▓▓  ▓▓ ┃
┃  ▓▓ ▓  ▓ ▓ ▓▓ ▓ ▓▓  ▓▓  ▓▓  ▓  ┃    ┃  ░    ░░░░░▓▓  ░▓▓   ▓▓▓▓▓  ▓▓ ┃
┃  ▓ ▓  ▓ ▓ ▓  ▓ ▓▓▓    ▓▓ ▓▓▓ ▓▓┃    ┃       ░░░░░     ▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓ ▓  ▓ ▓  ▓        ▓ ▓▓  ▓▓▓ ┃    ┃       ░░░░░          ▓▓▓▓  ▓▓▓ ┃
┃▓    ▓ ▓▓ ▓▓▓   ▓▓▓▓  ▓ ▓▓  ▓ ▓ ┃    ┃      ▓▓▓▓▓▓▓▓        ▓▓▓▓      ┃
┃▓▓▓▓▓ ▓▓▓▓  ▓▓   ▓  ▓▓▓▓ ▓      ┃    ┃▓▓▓   ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓      ┃
┃ ▓▓  ▓▓  ▓▓▓ ▓▓▓▓ ▓▓ ▓ ▓▓▓    ▓ ┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓      ▓▓▓ ▓▓▓ ▓▓ ▓ ▓ ▓ ▓  ▓▓▓ ┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓  ┃
┃▓▓▓▓▓▓ ▓▓▓▓   ▓▓    ▓ ▓▓▓▓▓ ▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓  ▓▓  ┃
┃    ▓▓▓▓   ▓ ▓▓   ▓ ▓▓  ▓▓      ┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓    ▓▓  ▓▓      ┃
┃▓▓▓▓ ▓ ▓▓   ▓▓▓▓▓▓   ▓  ▓  ▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓       ▓▓ ┃
┃▓▓▓▓▓▓ ▓▓   ▓ ▓▓▓   ▓▓▓   ▓▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓    ▓▓▓▓            ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓▓▓   ▓▓▓ ▓▓   ▓▓     ▓ ▓  ▓┃    ┃▓▓▓        ▓▓                   ┃
┃▓▓▓   ▓  ▓ ▓▓▓ ▓ ▓▓ ▓▓▓▓ ▓ ▓▓▓▓ ┃    ┃▓▓▓       ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓   ┃
┃▓▓▓ ▓    ▓▓    ▓▓    ▓▓ ▓▓▓▓    ┃    ┃▓▓▓      ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓   ▓    ▓  ▓▓▓▓▓▓ ▓▓▓▓▓▓▓ ▓   ┃    ┃▓▓▓      ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃  ▓ ▓ ▓▓▓▓▓  ▓▓ ▓ ▓▓▓▓ ▓  ▓ ▓ ▓ ┃    ┃        ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃▓   ▓  ▓ ▓ ▓▓    ▓▓   ▓ ▓ ▓  ▓  ┃    ┃        ▓▓▓▓          ▓▓▓▓▓     ┃
┃▓ ▓  ▓   ▓▓▓  ▓ ▓   ▓ ▓▓▓▓▓ ▓   ┃    ┃         ▓▓▓          ▓▓▓▓▓     ┃
┃ ▓     ▓  ▓▓ ▓▓   ▓  ▓ ▓ ▓  ▓▓▓▓┃    ┃         ▓▓▓          ▓▓▓▓  ▓▓▓▓┃
┃▓ ▓   ▓  ▓▓▓    ▓▓  ▓  ▓▓▓  ▓▓▓▓┃    ┃         ▓▓▓         ▓▓▓▓▓  ▓▓▓▓┃
┃    ▓   ▓▓▓   ▓▓  ▓▓ ▓▓▓▓▓    ▓ ┃    ┃        ▓▓▓         ▓▓▓▓▓▓      ┃
┃▓ ▓ ▓ ▓ ▓    ▓▓  ▓ ▓ ▓▓  ▓  ▓   ┃    ┃        ▓▓▓         ▓▓▓▓▓▓      ┃
┃▓▓   ▓▓ ▓▓ ▓▓▓      ▓  ▓▓    ▓▓ ┃    ┃▓▓    ▓▓▓▓▓▓▓        ▓▓▓▓    ▓▓ ┃
┃▓▓  ▓ ▓▓▓▓▓▓▓  ▓ ▓▓  ▓▓  ▓▓ ▓▓▓ ┃    ┃▓▓    ▓▓▓▓▓▓▓         ▓▓▓    ▓▓ ┃
┃▓  ▓  ▓▓ ▓▓ ▓ ▓  ▓ ▓   ▓▓  ▓ ▓▓▓┃    ┃      ▓▓▓▓▓▓▓          ▓▓    ▓▓ ┃
┃        ▓ ▓▓  ▓▓  ▓ ▓ ▓▓▓     ▓ ┃    ┃      ▓▓▓▓▓▓           ▓▓       ┃
┃ ▓▓ ▓ ▓▓▓▓▓▓▓  ▓▓ ▓▓    ▓  ▓  ▓ ┃    ┃     ▓▓▓▓▓▓▓    ▓▓▓             ┃
┃▓   ▓▓▓ ▓▓   ▓ ▓ ▓▓   ▓  ▓ ▓ ▓  ┃    ┃    ▓▓▓▓▓▓▓▓    ▓▓▓             ┃
┃▓▓  ▓▓ ▓▓ ▓▓ ▓▓ ▓▓▓▓ ▓ ▓   ▓ ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓ ░▓▓▓             ┃
┃▓  ▓  ▓   ▓ ▓ ▓  ▓▓   ▓▓▓▓▓▓▓  ▓┃    ┃      ░░   ▓▓▓  ▓▓▓   ▓▓▓▓▓▓▓   ┃
┃    ▓  ▓    ▓▓  ▓▓▓   ▓▓ ▓▓▓ ▓▓ ┃    ┃      ░░   ▓▓▓  ▓▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃  ▓ ▓▓▓▓▓ ▓▓▓▓  ▓▓▓▓ ▓▓   ▓▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓  ▓▓▓▓  ▓▓  ▓▓▓▓▓ ┃
┃  ▓   ▓ ▓▓ ▓ ▓ ▓   ▓   ▓    ▓▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓   ▓▓▓▓ ┃
┃ ▓▓▓▓▓▓▓ ▓▓ ▓▓   ▓▓▓▓ ▓ ▓  ▓   ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓     ▓▓ ┃
┃▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓▓▓  ▓▓▓   ▓▓ ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓   ▓▓ ▓▓ ┃
┃ ▓▓▓       ▓    ▓▓▓ ▓ ▓▓▓ ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ▓▓ ▓▓ ┃
┃▓  ▓ ▓▓▓ ▓ ▓ ▓▓▓▓  ▓   ▓        ┃    ┃  ▓▓▓▓▓▓▓▓▓▓  ▓▓▓               ┃
┃ ▓ ▓▓ ▓ ▓ ▓▓  ▓ ▓       ▓ ▓    ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓               ┃
┃ ▓   ▓▓ ▓▓▓▓▓▓▓▓ ▓▓▓   ▓ ▓   ▓  ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓             ┃
┃▓▓▓▓  ▓▓   ▓  ▓▓▓▓  ▓▓▓ ▓   ▓▓▓▓┃    ┃      ▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓┃
┃   ▓  ▓  ▓▓ ▓▓▓▓ ▓▓ ▓▓▓    ▓▓▓ ▓┃    ┃   ░  ▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓┃
┃▓▓ ▓▓ ▓    ▓ ▓▓  ▓▓▓  ▓        ▓┃    ┃   ▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓          ┃
┃▓  ▓▓▓▓ ▓▓▓ ▓▓▓  ▓▓ ▓▓  ▓▓▓ ▓  ▓┃    ┃   ▓▓▓▓     ▓▓▓  ▓▓             ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓▓   ▓ ▓▓  ▓  ▓ ▓  ▓▓▓▓ ▓▓▓ ┃    ┃  ▓▓                            ┃
┃▓ ▓  ▓    ▓ ▓▓  ▓  ▓▓ ▓  ▓ ▓  ▓ ┃    ┃ ▓▓▓               ▓▓▓          ┃
┃▓▓▓▓   ▓       ▓  ▓▓▓▓  ▓ ▓▓  ▓▓┃    ┃ ▓▓                ▓▓▓        ▓▓┃
┃     ▓  ▓ ▓ ▓  ▓▓   ▓▓ ▓ ▓ ▓▓▓ ▓┃    ┃               ▓▓   ▓▓     ▓▓▓▓▓┃
┃ ▓ ▓▓  ▓ ▓ ▓ ▓▓▓▓    ▓    ▓ ▓▓▓▓┃    ┃               ▓▓          ▓▓▓▓▓┃
┃   ▓   ▓▓▓▓     ▓▓ ▓  ▓▓       ▓┃    ┃        ▓▓▓▓▓▓▓▓▓▓              ┃
┃ ▓  ▓    ▓▓▓▓▓▓▓▓▓ ▓▓ ▓  ▓ ▓ ▓  ┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓            ┃
┃   ▓ ▓▓ ▓▓ ▓  ▓▓ ▓▓  ▓   ▓  ▓ ▓▓┃    ┃        ▓▓▓▓  ▓▓▓▓▓▓            ┃
┃▓▓▓    ▓▓  ▓  ▓▓  ▓▓   ▓▓ ▓▓    ┃    ┃ ▓▓▓    ▓▓    ▓▓▓▓▓▓     ▓▓▓    ┃
┃  ▓▓ ▓▓  ▓   ▓▓  ▓▓▓▓▓   ▓▓▓  ▓▓┃    ┃ ▓▓▓    ▓▓   ▓▓▓▓▓▓▓▓   ▓▓▓▓    ┃
┃▓▓▓ ▓   ▓ ▓▓ ▓▓ ▓ ▓ ▓  ▓▓▓ ▓    ┃    ┃ ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓     ┃
┃ ▓▓▓     ▓▓▓▓  ▓▓▓ ▓▓    ▓   ▓ ▓┃    ┃ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓   ░░░     ┃
┃ ▓ ▓  ▓ ▓▓  ▓▓▓ ▓ ▓▓▓  ▓ ▓ ▓    ┃    ┃ ░░░     ▓▓▓▓▓▓▓░▓▓▓▓   ░░░     ┃
┃▓ ▓ ▓ ▓▓ ▓ ▓▓▓    ▓   ▓▓▓ ▓ ▓  ▓┃    ┃ ░░░        ▓▓▓░      ▓▓░░░     ┃
┃ ▓ ▓▓  ▓      ▓ ▓   ▓ ▓  ▓▓ ▓  ▓┃    ┃ ░░░          ░░      ▓▓░░░     ┃
┃▓▓▓ ▓▓  ▓▓  ▓  ▓  ▓   ▓▓  ▓  ▓  ┃    ┃▓▓▓▓▓▓        ░░         ▓▓     ┃
┃▓▓ ▓ ▓▓ ▓ ▓▓▓▓▓ ▓▓▓      ▓▓ ▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓     ░▓▓▓      ▓▓     ┃
┃▓▓▓ ▓▓ ▓▓▓     ▓▓▓▓ ▓  ▓ ▓▓ ▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓      ▓▓▓     ▓▓▓▓▓   ┃
┃▓▓▓ ▓▓ ▓ ▓    ▓  ▓▓ ▓ ▓▓▓  ▓▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓      ▓▓▓   ▓▓▓  ▓▓   ┃
┃ ▓ ▓▓ ▓  ▓   ▓ ▓▓  ▓▓ ▓ ▓  ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓            ▓▓▓  ▓▓   ┃
┃ ▓▓▓▓▓▓▓▓▓   ▓    ▓   ▓ ▓▓▓▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓              ▓▓▓▓▓   ┃
┃  ▓ ▓▓    ▓ ▓   ▓  ▓    ▓ ▓  ▓▓▓┃    ┃   ▓▓▓                    ▓▓▓▓▓▓┃
┃    ▓  ▓▓   ▓      ▓▓▓▓▓   ▓▓▓▓▓┃    ┃                   ▓▓▓▓▓   ▓▓▓▓▓┃
┃     ▓   ▓▓   ▓     ▓ ▓▓  ▓▓▓▓  ┃    ┃         ▓▓        ▓▓▓▓▓   ▓▓▓▓ ┃
┃  ▓▓ ▓▓ ▓▓▓   ▓▓▓▓ ▓▓▓▓ ▓   ▓▓▓ ┃    ┃  ▓▓ ▓▓  ▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓▓ ┃
┃▓ ▓▓ ▓▓    ▓▓   ▓▓▓▓ ▓▓  ▓▓ ▓ ▓▓┃    ┃  ▓▓ ▓▓        ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓┃
┃▓     ▓    ▓  ▓▓   ▓ ▓▓   ▓▓   ▓┃    ┃      ▓        ▓▓   ▓▓▓   ▓▓▓▓▓▓┃
┃  ▓▓▓ ▓▓▓ ▓▓   ▓▓   ▓   ▓  ▓▓ ▓▓┃    ┃      ▓▓▓      ▓▓         ▓▓▓▓▓▓┃
┃   ▓  ▓▓▓     ▓▓      ▓▓▓▓▓▓▓ ▓ ┃    ┃      ▓▓▓     ▓▓▓       ▓▓▓▓▓▓▓ ┃
┃     ▓▓▓▓ ▓▓ ▓ ▓▓    ▓  ▓ ▓▓▓▓▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓ ┃
┃▓ ▓ ▓ ▓ ▓▓▓▓▓▓▓▓▓ ▓▓▓   ▓▓▓▓▓▓ ▓┃    ┃     ░▓▓▓▓▓▓▓▓▓▓▓ ▓▓    ▓▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓  ▓▓  ▓▓   ▓  ▓▓┃    ┃    ░░▓▓▓▓▓▓▓▓▓   ▓▓            ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓ ▓▓ ▓ ▓▓  ▓▓ ▓ ▓▓▓▓▓ ▓  ▓▓▓┃    ┃   ▓▓░░▓▓           ▓▓▓▓     ▓▓ ┃
┃   ▓▓▓ ▓▓▓  ▓▓ ▓  ▓ ▓▓▓ ▓ ▓ ▓▓▓ ┃    ┃   ▓▓░░▓▓   ▓▓▓▓    ▓▓▓▓    ▓▓▓ ┃
┃   ▓      ▓ ▓▓▓▓  ▓  ▓     ▓  ▓ ┃    ┃            ▓▓▓▓           ▓▓▓▓ ┃
┃  ▓  ▓  ▓ ▓  ▓▓  ▓▓  ▓ ▓▓▓▓▓▓▓ ▓┃    ┃             ▓▓          ▓▓▓▓▓▓ ┃
┃ ▓ ▓  ▓▓ ▓   ▓▓ ▓   ▓ ▓  ▓  ▓▓▓▓┃    ┃       ▓▓▓   ▓▓          ▓▓▓▓▓▓ ┃
┃ ▓ ▓▓▓ ▓ ▓▓▓▓   ▓▓▓ ▓   ▓ ▓▓▓▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓ ┃
┃     ▓▓ ▓▓▓▓ ▓▓▓▓▓▓ ▓ ▓  ▓  ▓▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓ ┃
┃▓▓ ▓▓ ▓   ▓▓▓  ▓▓  ▓▓     ▓▓▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓     ▓▓▓▓▓ ┃
┃▓▓▓▓▓▓▓▓▓ ▓ ▓▓ ▓▓   ▓▓   ▓▓▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓   ▓▓    ▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓▓  ▓▓ ▓      ▓▓ ▓ ▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓    ▓▓▓   ▓▓▓▓▓ ┃
┃▓ ▓   ▓ ▓▓ ▓▓▓ ▓ ▓ ▓▓▓▓ ▓ ▓ ▓▓▓▓┃    ┃       ▓▓▓▓▓▓▓▓▓   ▓▓▓▓    ▓▓▓▓ ┃
┃▓▓ ▓    ▓ ▓ ▓▓▓▓ ▓ ▓ ▓ ▓  ▓ ▓ ▓ ┃    ┃        ▓▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓ ┃
┃  ▓▓ ▓ ▓▓▓ ▓ ▓▓▓ ▓ ▓▓▓ ▓▓▓  ▓▓▓ ┃    ┃        ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓░▓▓▓▓▓ ┃
┃▓   ▓   ▓▓  ▓▓ ▓ ▓  ▓ ▓ ▓ ▓▓▓▓▓▓┃    ┃        ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓        ▓▓ ▓   ▓  ▓▓▓ ▓ ▓  ▓▓┃    ┃▓▓▓        ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓      ▓▓▓▓▓▓ ▓▓▓ ▓▓  ▓▓ ▓ ┃    ┃▓▓▓▓▓      ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓▓▓ ▓ ▓▓▓    ▓      ▓ ▓▓   ▓┃    ┃▓▓▓▓▓     ▓▓▓▓         ▓▓▓▓▓    ┃
┃          ▓ ▓▓ ▓  ▓▓▓  ▓▓▓▓ ▓  ▓┃    ┃          ▓▓▓     ▓▓▓  ▓▓▓▓▓    ┃
┃ ▓ ▓  ▓  ▓▓▓▓  ▓ ▓▓▓▓▓▓   ▓ ▓   ┃    ┃          ▓▓▓     ▓▓▓▓▓▓▓▓▓     ┃
┃▓     ▓ ▓       ▓    ▓▓▓ ▓▓   ▓▓┃    ┃      ▓▓          ▓▓▓▓▓  ▓▓   ▓▓┃
┃     ▓▓▓ ▓▓ ▓▓ ▓▓▓▓ ▓▓   ▓▓  ▓▓▓┃    ┃     ▓▓▓     ▓▓▓▓▓  ▓▓   ▓▓  ▓▓▓┃
┃▓▓▓▓ ▓▓▓     ▓▓▓▓ ▓  ▓     ▓ ▓▓ ┃    ┃ ▓▓  ▓▓▓     ▓▓▓▓▓  ▓▓       ▓▓ ┃
┃ ▓▓ ▓ ▓    ▓▓       ▓▓▓    ▓ ▓▓ ┃    ┃ ▓▓          ░░░▓░  ▓▓       ▓▓ ┃
┃▓ ▓  ▓    ▓ ▓ ▓ ▓▓ ▓ ▓    ▓   ▓▓┃    ┃ ▓▓          ░░▓▓▓░░▓▓       ▓▓▓┃
┃▓ ▓    ▓   ▓ ▓ ▓ ▓▓ ▓▓ ▓ ▓  ▓ ▓▓┃    ┃            ░░▓▓▓▓░░▓▓       ▓▓▓┃
┃     ▓▓▓▓ ▓ ▓ ▓▓▓▓ ▓▓ ▓▓   ▓▓▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓     ▓▓▓▓ ┃
┃ ▓  ▓▓  ▓▓ ▓▓▓  ▓▓   ▓ ▓▓▓▓▓    ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓▓   ┃
┃▓▓▓▓▓  ▓▓▓▓▓▓ ▓ ▓ ▓▓▓▓   ▓  ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓▓   ┃
┃ ▓▓▓▓▓▓▓  ▓ ▓  ▓▓  ▓  ▓ ▓ ▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓   ▓▓  ▓▓▓▓▓   ┃
┃ ▓▓   ▓   ▓▓▓▓▓▓▓   ▓▓  ▓▓▓▓   ▓┃    ┃ ▓▓       ▓▓▓▓▓▓▓       ▓▓▓▓▓   ┃
┃▓     ▓ ▓▓▓▓ ▓▓    ▓  ▓▓ ▓ ▓ ▓ ▓┃    ┃          ▓▓▓▓▓                 ┃
┃▓▓▓  ▓   ▓    ▓ ▓▓ ▓  ▓   ▓ ▓▓▓ ┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓   ▓  ▓▓▓▓▓  ▓▓ ▓    ▓▓  ▓ ▓▓  ┃    ┃        ▓▓▓▓                ▓▓  ┃
┃▓▓    ▓ ▓ ▓▓ ▓ ▓   ▓▓▓    ▓ ▓▓▓ ┃    ┃▓▓     ▓▓▓▓▓▓             ▓▓▓▓▓ ┃
┃▓▓▓ ▓ ▓▓▓▓▓▓▓    ▓  ▓  ▓ ▓▓▓ ▓▓ ┃    ┃▓▓▓    ▓▓▓▓▓▓           ▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓ ▓ ▓   ▓  ▓       ▓▓▓▓▓▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓              ▓▓▓▓▓▓▓ ┃
┃▓  ▓▓▓ ▓ ▓▓  ▓▓ ▓▓ ▓ ▓ ▓     ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓                 ┃
┃ ▓▓▓▓▓  ▓▓ ▓ ▓▓  ▓ ▓▓     ▓ ▓ ▓ ┃    ┃  ▓▓▓▓  ▓▓   ▓▓░░░▓▓▓▓          ┃
┃    ▓   ▓   ▓ ▓ ▓ ▓▓▓▓▓▓  ▓   ▓▓┃    ┃    ▓▓       ░░░░░▓▓▓▓          ┃
┃▓▓  ▓▓▓     ▓  ▓  ▓▓▓ ▓      ▓  ┃    ┃    ▓▓       ░░░░░▓▓▓▓          ┃
┃ ▓ ▓▓ ▓ ▓▓ ▓▓▓ ▓ ▓▓▓▓▓   ▓▓ ▓  ▓┃    ┃▓▓▓▓▓▓ ▓▓▓░░▓░░░░░▓▓▓▓   ▓▓     ┃
┃▓▓ ▓▓  ▓ ▓▓  ▓ ▓ ▓ ▓▓ ▓  ▓▓  ▓ ▓┃    ┃▓▓▓▓▓  ▓▓▓░░▓░░░░░▓▓▓▓   ▓▓     ┃
┃▓ ▓▓   ▓ ▓ ▓▓ ▓ ▓   ▓ ▓    ▓   ▓┃    ┃       ▓▓▓░░░      ▓▓▓          ┃
┃     ▓ ▓▓▓  ▓     ▓ ▓▓ ▓ ▓  ▓▓▓▓┃    ┃       ▓▓▓         ▓▓▓          ┃
┃▓ ▓     ▓ ▓ ▓   ▓ ▓▓ ▓     ▓    ┃    ┃        ▓▓        ▓▓▓▓          ┃
┃▓   ▓ ▓ ▓▓   ▓  ▓  ▓▓▓  ▓   ▓▓ ▓┃    ┃        ▓▓▓       ▓▓▓▓          ┃
┃ ▓▓▓ ▓▓ ▓ ▓▓▓▓ ▓ ▓▓ ▓▓   ▓▓ ▓  ▓┃    ┃  ▓▓▓   ▓▓▓▓       ▓▓▓    ▓▓▓   ┃
┃▓ ▓▓▓  ▓▓ ▓▓    ▓   ▓▓▓▓  ▓▓▓   ┃    ┃  ▓▓▓   ▓▓▓▓       ▓▓▓▓▓  ▓▓▓   ┃
┃   ▓    ▓▓▓   ▓▓▓▓ ▓ ▓▓▓ ▓  ▓▓▓ ┃    ┃  ▓▓▓   ▓▓▓     ▓▓▓▓▓▓▓▓    ▓▓▓ ┃
┃▓ ▓▓▓▓  ▓    ▓  ▓▓▓ ▓▓▓▓     ▓▓ ┃    ┃   ▓▓▓  ▓▓▓     ▓▓▓▓▓▓▓▓    ▓▓▓ ┃
┃▓   ▓▓▓ ▓▓▓▓ ▓   ▓▓▓ ▓  ▓ ▓ ▓ ▓▓┃    ┃    ▓▓░░▓▓▓▓▓    ▓▓▓▓▓      ▓▓▓ ┃
┃▓   ▓ ▓ ▓▓▓▓ ▓▓▓ ▓▓▓▓   ▓  ▓  ▓ ┃    ┃     ░░░▓▓▓▓▓▓   ▓▓▓▓▓      ▓▓▓ ┃
┃▓▓▓  ▓ ▓   ▓▓     ▓ ▓▓▓▓▓  ▓▓ ▓▓┃    ┃      ░░▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓  ▓▓▓▓ ┃
┃   ▓▓   ▓▓  ▓▓  ▓▓   ▓  ▓▓▓ ▓▓  ┃    ┃          ▓▓▓▓  ▓▓▓  ▓▓▓▓▓▓▓▓   ┃
┃ ▓  ▓▓   ▓ ▓▓ ▓▓▓▓▓   ▓▓  ▓▓    ┃    ┃   ▓▓     ▓▓▓▓▓▓▓▓▓   ▓▓▓▓      ┃
┃   ▓▓     ▓ ▓▓ ▓▓▓ ▓ ▓ ▓▓       ┃    ┃   ▓▓     ░▓▓▓▓▓▓▓▓    ▓▓       ┃
┃ ▓▓▓▓ ▓ ▓ ▓ ▓▓▓ ▓▓ ▓   ▓▓▓  ▓▓ ▓┃    ┃   ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓   ▓▓       ┃
┃▓ ▓  ▓▓▓  ▓   ▓  ▓▓▓▓▓     ▓▓ ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓        ▓▓┃
┃▓▓ ▓▓▓▓▓▓▓▓ ▓▓   ▓   ▓▓▓      ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓      ▓▓┃
┃   ▓  ▓  ▓ ▓ ▓▓      ▓▓▓▓▓ ▓▓   ┃    ┃   ▓▓▓▓▓   ▓▓▓▓      ▓▓▓▓▓      ┃
┃▓ ▓▓▓▓ ▓  ▓▓▓▓  ▓  ▓▓▓▓▓▓▓  ▓  ▓┃    ┃   ▓▓▓▓▓    ▓▓▓    ▓▓▓▓▓▓▓      ┃
┃▓ ▓  ▓▓ ▓▓  ▓▓▓  ▓▓▓▓▓ ▓▓▓  ▓▓▓▓┃    ┃            ▓▓▓    ▓▓▓▓▓▓▓      ┃
┃ ▓     ▓ ▓    ▓▓ ▓ ▓ ▓   ▓     ▓┃    ┃             ▓▓                 ┃
┃   ▓▓  ▓▓   ▓▓▓ ▓      ▓▓ ▓ ▓▓ ▓┃    ┃             ▓▓                 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓   ▓▓ ▓▓▓▓▓   ▓ ▓ ▓   ▓▓  ▓┃    ┃▓▓▓▓▓        ▓▓▓                ┃
┃▓▓▓▓▓  ▓▓  ▓ ▓ ▓▓▓    ▓ ▓▓▓ ▓▓▓▓┃    ┃▓▓▓▓▓  ▓▓    ▓▓▓▓▓              ┃
┃▓▓     ▓▓ ▓   ▓▓▓▓▓ ▓▓    ▓   ▓ ┃    ┃▓▓     ▓▓     ▓▓▓▓           ░  ┃
┃ ▓   ▓▓   ▓ ▓ ▓▓      ▓▓▓    ▓  ┃    ┃       ▓▓     ▓▓▓▓     ▓▓    ░░ ┃
┃  ▓   ▓▓ ▓      ▓▓ ▓▓▓ ▓▓▓▓▓▓▓▓▓┃    ┃        ░      ▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃  ▓▓  ▓ ▓▓     ▓▓ ▓▓  ▓▓▓▓▓ ▓  ▓┃    ┃               ▓▓      ▓▓▓▓▓▓▓▓▓┃
┃▓  ▓ ▓ ▓ ▓▓▓▓▓▓▓   ▓   ▓ ▓▓▓▓▓▓▓┃    ┃         ▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓┃
┃▓▓ ▓    ▓▓▓ ▓ ▓▓    ▓▓  ▓ ▓▓▓▓▓▓┃    ┃▓▓▓      ▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓┃
┃ ▓▓    ▓  ▓▓ ▓▓▓    ▓ ▓   ▓▓▓▓ ▓┃    ┃▓▓▓      ▓▓▓▓▓▓▓    ▓▓    ▓▓▓▓▓▓┃
┃▓ ▓▓ ▓ ▓ ▓ ▓    ▓▓▓ ▓▓     ▓ ▓▓▓┃    ┃▓▓▓              ▓▓▓▓▓    ▓▓▓▓▓▓┃
┃▓▓▓  ▓▓  ▓   ▓   ▓▓  ▓ ▓▓ ▓ ▓ ▓▓┃    ┃▓▓▓              ▓▓▓▓▓▓▓  ▓▓▓▓▓▓┃
┃▓ ▓ ▓ ▓ ▓ ▓  ▓  ▓  ▓▓▓▓▓  ▓▓▓▓▓ ┃    ┃▓▓▓▓░░            ▓▓▓▓▓▓   ▓▓▓▓ ┃
┃▓  ▓ ▓      ▓▓▓▓▓ ▓ ▓    ▓ ▓  ▓ ┃    ┃▓▓▓▓░       ▓▓▓   ░▓▓▓▓▓     ░░ ┃
┃▓▓▓ ▓▓▓▓▓  ▓▓ ▓   ▓▓ ▓▓▓▓    ▓ ▓┃    ┃▓▓▓▓       ▓▓▓▓   ░░▓▓▓▓     ░░ ┃
┃  ▓▓ ▓  ▓  ▓▓▓▓ ▓▓    ▓▓  ▓▓▓▓▓ ┃    ┃  ▓▓       ▓▓▓▓  ▓▓   ▓▓     ░░ ┃
┃   ▓   ▓ ▓▓▓ ▓  ▓ ▓▓  ▓ ▓▓▓   ▓ ┃    ┃          ▓▓▓▓▓▓▓▓▓          ░░ ┃
┃▓ ▓  ▓▓   ▓▓▓ ▓▓▓ ▓ ▓▓    ▓ ▓ ▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓            ░░ ┃
┃ ▓▓   ▓▓▓    ▓▓    ▓ ▓ ▓▓ ▓  ▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓▓      ▓▓▓▓    ░░ ┃
┃▓ ▓ ▓  ▓▓▓▓▓▓▓▓  ▓ ▓ ▓▓▓▓    ▓▓▓┃    ┃      ▓▓▓▓▓▓▓▓▓      ▓▓▓▓    ▓▓ ┃
┃ ▓  ▓ ▓▓ ▓ ▓▓ ▓   ▓   ▓▓▓ ▓ ▓▓▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓  ▓▓▓ ┃
┃▓▓ ▓   ▓  ▓  ▓     ▓ ▓   ▓▓ ▓▓▓ ┃    ┃      ▓▓  ░░        ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓  ▓▓▓  ▓▓ ▓▓    ▓▓ ▓ ▓▓ ▓ ▓▓ ┃    ┃      ▓▓  ░░       ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓  ▓   ▓▓▓  ▓    ▓▓▓▓ ▓▓  ▓   ▓┃    ┃         ░▓▓▓▓     ▓▓▓▓▓▓▓▓▓    ┃
┃  ▓  ▓ ▓  ▓▓▓▓ ▓▓  ▓ ▓▓▓ ▓▓ ▓▓  ┃    ┃ ░        ▓▓▓▓     ▓▓▓▓▓▓▓▓     ┃
┃ ▓▓ ▓  ▓▓ ▓    ▓ ▓ ▓  ▓▓ ▓▓▓ ▓  ┃    ┃ ▓▓         ▓▓        ▓▓▓▓▓     ┃
┃ ▓         ▓ ▓▓▓  ▓     ▓      ▓┃    ┃ ▓▓         ▓▓▓▓                ┃
┃  ▓▓    ▓   ▓ ▓▓▓▓  ▓▓▓▓    ▓ ▓▓┃    ┃ ▓▓▓        ▓▓▓▓                ┃
┃ ▓▓▓▓▓▓     ▓▓    ▓   ▓    ▓▓   ┃    ┃ ▓▓▓        ▓▓                  ┃
┃▓        ▓  ▓▓     ▓▓      ▓ ▓▓ ┃    ┃  ▓▓        ▓▓                  ┃
┃▓▓▓▓▓   ▓▓   ▓▓ ▓▓  ▓▓▓▓    ▓ ▓ ┃    ┃  ▓▓           ▓▓▓▓▓▓▓▓▓     ▓▓ ┃
┃ ▓ ▓ ▓▓▓   ▓   ▓▓▓▓▓▓▓ ▓▓▓ ▓▓▓▓▓┃    ┃  ▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓▓   ▓▓ ┃
┃  ▓▓▓▓▓     ▓▓ ▓  ▓▓  ▓ ▓▓▓  ▓▓ ┃    ┃   ▓▓▓▓           ▓▓   ▓▓▓   ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓▓ ▓ ▓▓  ▓▓▓ ▓▓   ▓ ▓    ▓ ▓ ┃    ┃ ▓▓▓    ▓▓    ▓▓▓               ┃
┃▓▓ ▓   ▓▓▓    ▓▓▓  ▓ ▓   ▓ ▓▓▓▓▓┃    ┃ ▓▓▓    ▓▓    ▓▓▓          ▓▓▓  ┃
┃  ▓▓ ▓▓    ▓▓ ▓▓▓ ▓▓ ▓   ▓▓ ▓  ▓┃    ┃ ▓▓▓▓▓▓▓      ▓▓▓        ▓▓▓▓▓  ┃
┃▓ ▓▓▓ ▓ ▓    ▓▓ ▓    ▓▓▓▓ ▓ ▓ ▓ ┃    ┃  ▓▓▓▓▓▓      ▓▓▓    ▓▓▓▓▓  ░░  ┃
┃ ▓  ▓▓▓▓▓  ▓  ▓ ▓▓▓▓▓▓▓▓▓    ▓  ┃    ┃    ▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓  ░░  ┃
┃    ▓▓   ▓▓▓ ▓  ▓      ▓▓▓  ▓▓  ┃    ┃    ▓▓▓         ▓      ▓▓▓  ▓▓  ┃
┃ ▓▓ ▓▓▓         ▓  ▓   ▓▓▓ ▓▓▓▓▓┃    ┃    ▓▓▓         ▓      ▓▓▓▓▓▓▓  ┃
┃ ▓ ▓ ▓▓  ▓▓ ▓ ▓▓▓ ▓▓▓ ▓▓ ▓▓ ▓   ┃    ┃    ▓▓▓  ▓▓▓    ▓     ▓▓▓▓▓▓▓▓  ┃
┃    ▓ ▓▓▓▓▓▓ ▓  ▓     ▓▓ ▓▓  ▓ ▓┃    ┃    ▓▓▓▓▓▓▓▓▓   ▓     ▓▓▓▓▓▓▓░  ┃
┃▓ ▓ ▓  ▓▓ ▓  ▓  ▓ ▓ ▓▓  ▓ ▓▓  ▓▓┃    ┃       ▓▓▓▓▓▓▓  ▓▓      ▓▓▓  ▓▓▓┃
┃  ▓ ▓▓  ▓▓▓▓ ▓ ▓▓▓▓▓  ▓ ▓▓ ▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓▓  ▓▓      ▓▓▓  ▓▓▓┃
┃ ▓▓ ▓  ▓▓▓ ▓▓▓ ▓  ▓  ▓  ▓▓   ▓ ▓┃    ┃        ▓▓▓▓▓▓   ▓      ▓▓   ▓▓▓┃
┃  ▓ ▓    ▓ ▓     ▓  ▓▓    ▓▓▓▓▓▓┃    ┃          ▓▓▓▓   ▓▓▓▓▓       ▓▓▓┃
┃▓  ▓ ▓ ▓  ▓▓ ▓ ▓▓▓▓▓▓ ▓▓     ▓ ▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓┃
┃  ▓   ▓ ▓ ▓ ▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓ ▓  ▓┃    ┃         ░░░░▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓┃
┃▓▓     ▓▓▓ ▓  ▓▓▓      ▓▓▓ ▓  ▓▓┃    ┃      ▓▓░     ▓▓▓      ▓▓░▓▓▓▓▓▓┃
┃  ▓▓▓▓▓▓  ▓▓    ▓▓ ▓▓  ▓    ▓▓▓ ┃    ┃  ▓▓▓▓▓▓               ▓  ▓▓▓▓▓ ┃
┃  ▓▓  ▓  ▓  ▓▓    ▓ ▓▓ ▓  ▓▓ ▓  ┃    ┃  ▓▓▓▓             ▓▓▓▓▓  ▓▓▓▓▓ ┃
┃  ▓  ▓     ▓ ▓▓ ▓   ▓▓▓▓  ▓ ▓▓ ▓┃    ┃           ▓▓▓▓    ▓▓▓▓▓  ▓▓▓▓▓ ┃
┃  ▓   ▓ ▓▓ ▓ ▓▓▓ ▓▓▓▓   ▓▓▓ ▓ ▓▓┃    ┃         ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓ ▓▓▓   ▓▓▓▓▓   ▓   ▓ ▓▓▓ ▓▓   ┃    ┃  ▓▓▓    ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃  ▓▓▓   ▓    ▓▓   ▓▓▓ ▓  ▓▓ ▓▓ ▓┃    ┃ ▓▓▓▓    ▓  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓  ▓▓▓  ▓▓    ▓▓  ▓▓▓ ▓ ▓   ┃    ┃ ▓▓▓▓  ▓▓▓  ▓▓    ▓▓   ▓▓▓▓▓▓   ┃
┃ ▓▓▓  ▓▓  ▓▓▓ ▓    ▓    ▓ ▓▓  ▓▓┃    ┃ ▓▓▓▓░░▓▓▓▓▓▓▓         ▓▓▓▓▓  ▓▓┃
┃▓ ▓▓▓ ▓ ▓▓▓     ▓ ▓   ▓ ▓▓▓ ▓ ▓▓┃    ┃ ▓▓▓▓░░▓▓▓▓            ▓▓▓▓   ▓▓┃
┃ ▓ ▓ ▓ ▓         ▓▓ ▓▓▓▓  ▓    ▓┃    ┃  ▓▓▓░░░░          ▓▓▓▓▓  ▓   ░░┃
┃   ▓▓   ▓▓ ▓   ▓  ▓ ▓  ▓  ▓  ▓ ▓┃    ┃  ▓▓▓░░░░        ▓▓▓▓▓▓▓  ▓   ░ ┃
┃ ▓▓▓▓▓ ▓   ▓▓    ▓▓ ▓▓ ▓ ▓▓ ▓▓▓ ┃    ┃  ▓▓▓  ░░        ▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓     ▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓┃    ┃       ▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃   ▓   ▓▓▓▓ ▓▓   ▓▓   ▓      ▓▓ ┃    ┃       ▓▓▓▓▓▓▓   ▓▓▓▓▓          ┃
┃▓ ▓▓   ▓▓ ▓ ▓ ▓▓   ▓ ▓▓  ▓     ▓┃    ┃       ▓▓▓▓▓▓▓▓                 ┃
┃    ▓ ▓ ▓▓▓▓▓▓▓ ▓   ▓  ▓ ▓ ▓  ▓ ┃    ┃       ▓▓▓▓▓▓▓▓                 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓ ▓▓ ▓  ▓▓ ▓▓▓ ▓     ▓▓    ▓┃    ┃   ▓▓       ▓▓▓▓                ┃
┃ ▓ ▓▓  ▓  ▓▓▓▓ ▓  ▓▓▓   ▓▓  ▓  ▓┃    ┃   ▓▓    ▓▓▓▓▓▓▓  ▓▓▓           ┃
┃      ▓ ▓▓▓  ▓▓▓   ▓▓▓ ▓    ▓   ┃    ┃         ▓▓▓▓▓▓▓  ▓▓▓           ┃
┃  ▓  ▓   ▓ ▓▓  ▓ ▓▓ ▓   ▓ ▓    ▓┃    ┃          ▓▓▓▓▓░▓▓▓▓            ┃
┃▓▓ ▓  ▓   ▓▓  ▓  ▓▓      ▓ ▓   ▓┃    ┃          ▓▓▓▓░▓▓▓▓             ┃
┃ ▓ ▓▓ ▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓ ▓▓ ▓     ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓        ┃
┃  ▓▓▓▓▓ ▓▓▓   ▓  ▓  ▓▓▓▓▓ ▓   ▓▓┃    ┃   ▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ▓▓▓        ┃
┃    ▓  ▓    ▓▓ ▓▓▓ ▓  ▓  ▓  ▓▓▓ ┃    ┃   ▓▓        ▓▓▓▓▓    ▓▓        ┃
┃▓ ▓▓▓  ▓ ▓   ▓▓▓▓     ▓ ▓  ▓    ┃    ┃   ▓▓        ▓▓▓▓▓              ┃
┃ ▓   ▓ ▓ ▓ ▓▓   ▓ ▓▓  ▓▓   ▓▓ ▓▓┃    ┃        ▓▓▓▓▓  ▓▓▓▓▓            ┃
┃▓     ▓ ▓▓▓▓   ▓ ▓▓▓▓    ▓ ▓    ┃    ┃        ▓▓▓▓▓  ░▓▓▓▓            ┃
┃▓ ▓ ▓   ▓ ▓ ▓▓ ▓      ▓  ▓▓ ▓▓  ┃    ┃        ▓▓▓▓▓▓▓▓▓        ▓▓▓▓   ┃
┃▓ ▓  ▓ ▓▓   ▓▓▓▓▓▓       ▓▓▓▓ ▓▓┃    ┃▓▓▓         ▓▓▓▓▓        ▓▓▓▓▓  ┃
┃ ▓▓▓  ▓     ▓▓▓  ▓ ▓▓    ▓   ▓ ▓┃    ┃▓▓▓         ▓▓▓    ▓▓    ▓▓▓▓▓▓▓┃
┃▓▓ ▓  ▓▓▓▓▓▓▓ ▓    ▓▓ ▓▓ ▓▓ ▓▓▓▓┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓    ▓▓▓▓    ▓▓▓▓▓┃
┃▓▓▓  ▓▓  ▓ ▓ ▓ ▓   ▓ ▓▓    ▓ ▓▓ ┃    ┃▓▓▓    ▓▓▓▓▓▓▓     ▓▓▓▓    ▓▓▓▓▓┃
┃▓▓▓   ▓ ▓▓▓▓   ▓ ▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓┃    ┃▓▓▓     ▓▓▓▓▓▓     ▓▓▓▓ ░░░▓▓▓▓▓┃
┃▓▓ ▓    ▓   ▓ ▓ ▓▓▓  ▓▓ ▓ ▓▓  ▓▓┃    ┃▓▓▓     ▓▓▓▓▓▓▓░░░       ░░▓▓▓▓▓┃
┃ ▓▓▓▓  ▓ ▓▓▓▓▓▓▓ ▓      ▓  ▓▓▓ ▓┃    ┃▓▓▓▓▓   ▓▓▓▓▓▓▓░░░░        ▓▓▓▓▓┃
┃▓▓▓ ▓▓▓▓▓▓▓▓ ▓  ▓ ▓▓▓  ▓   ▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓┃
┃▓▓▓ ▓▓▓▓ ▓ ▓  ▓ ▓▓▓▓     ▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓┃
┃▓ ▓▓▓  ▓    ▓▓▓  ▓▓▓   ▓▓▓▓▓  ▓▓┃    ┃ ▓▓▓▓  ▓▓   ▓▓▓▓▓▓▓▓    ▓▓▓▓  ▓▓┃
┃ ▓▓▓▓  ▓▓▓  ▓▓  ▓▓ ▓ ▓   ▓ ▓  ▓ ┃    ┃ ▓▓▓▓       ▓▓▓▓▓▓▓     ▓▓▓▓  ▓▓┃
┃ ▓▓▓ ▓      ▓▓▓▓ ▓   ▓ ▓▓▓▓▓▓▓▓▓┃    ┃ ▓▓▓▓       ▓▓▓▓       ▓▓▓▓▓▓▓▓ ┃
┃   ▓  ▓  ▓▓▓▓▓▓▓   ▓▓▓ ▓   ▓▓   ┃    ┃   ▓▓    ▓▓▓▓▓▓▓   ▓▓▓▓▓▓  ▓▓▓  ┃
┃▓▓ ▓ ▓▓ ▓▓▓▓  ▓▓   ▓ ▓ ▓▓   ▓▓ ▓┃    ┃   ▓▓░░░▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓   ▓▓  ┃
┃   ▓ ▓  ▓▓ ▓▓  ▓   ▓▓▓▓▓▓ ▓  ▓ ▓┃    ┃   ▓▓░░░▓▓▓▓▓      ▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓ ▓ ▓▓  ▓   ▓▓ ▓▓▓▓▓▓▓▓   ▓▓┃    ┃ ▓▓▓▓░░░▓▓▓▓▓      ▓▓▓▓▓▓▓      ┃
┃ ▓▓▓   ▓ ▓▓▓▓▓   ▓   ▓▓▓  ▓ ▓▓ ▓┃    ┃ ▓▓▓    ▓▓▓▓▓   ▓▓▓▓▓▓▓▓    ▓▓  ┃
┃▓ ▓▓▓     ▓▓▓ ▓ ▓▓▓ ▓▓     ▓▓▓▓ ┃    ┃ ▓▓▓      ▓▓▓░░▓▓▓▓▓▓▓▓     ▓▓  ┃
┃▓▓          ▓▓ ▓▓▓▓▓  ▓   ▓     ┃    ┃           ▓▓░░▓▓▓▓▓            ┃
┃▓ ▓▓▓ ▓ ▓▓ ▓▓  ▓▓  ▓▓ ▓▓▓▓▓  ▓▓▓┃    ┃               ▓▓               ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓      ▓  ▓ ▓  ▓ ▓ ▓   ▓▓▓▓ ▓ ▓┃    ┃                        ▓▓▓     ┃
┃  ▓ ▓▓   ▓▓ ▓▓▓▓ ▓ ▓  ▓▓▓ ▓ ▓▓▓ ┃    ┃                       ▓▓▓▓░    ┃
┃▓  ▓ ▓▓▓▓     ▓ ▓    ▓ ▓▓ ▓   ▓ ┃    ┃   ▓▓▓▓▓               ▓▓▓▓     ┃
┃  ▓▓▓▓▓▓ ▓▓ ▓   ▓ ▓▓     ▓ ▓▓▓  ┃    ┃   ▓▓▓▓▓       ▓▓▓▓▓   ▓▓▓      ┃
┃   ▓▓▓  ▓    ▓ ▓▓▓▓▓▓▓ ▓▓      ▓┃    ┃   ▓▓▓▓▓▓      ▓▓▓▓▓░░▓▓▓▓      ┃
┃     ▓ ▓ ▓ ▓▓  ▓ ▓  ▓ ▓ ▓▓ ▓▓▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓      ┃
┃▓  ▓▓ ▓ ▓▓▓▓ ▓ ▓▓ ▓▓  ▓▓▓▓     ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓      ┃
┃  ▓ ▓▓ ▓▓  ▓ ▓▓  ▓ ▓▓ ▓ ▓  ▓▓  ▓┃    ┃      ░░▓▓▓▓▓▓  ▓▓▓▓░░▓▓▓▓      ┃
┃▓▓▓▓  ▓  ▓  ▓   ▓ ▓  ▓▓▓▓▓▓ ▓▓▓▓┃    ┃  ▓▓     ▓▓▓▓▓  ░▓  ░░▓▓▓▓▓▓▓▓▓▓┃
┃  ▓      ▓▓▓ ▓  ▓▓  ▓  ▓▓ ▓ ▓ ▓▓┃    ┃  ▓▓     ▓▓▓▓▓  ▓▓   ░▓▓▓▓▓  ▓▓▓┃
┃  ▓▓▓  ▓ ▓ ▓▓▓  ▓▓   ▓ ▓  ▓   ▓▓┃    ┃  ▓▓     ▓▓▓▓▓  ▓▓      ░░░   ▓▓┃
┃     ▓▓▓ ▓▓ ▓▓ ▓▓ ▓▓▓   ▓▓ ▓▓ ▓ ┃    ┃         ▓▓▓▓▓▓▓▓▓      ░░░     ┃
┃▓▓       ▓▓▓▓ ▓▓▓ ▓  ▓▓ ▓ ▓▓  ▓ ┃    ┃         ▓▓▓▓▓▓▓▓        ░░▓▓   ┃
┃▓  ▓▓▓  ▓▓▓▓ ▓▓▓   ▓  ▓▓    ▓▓  ┃    ┃   ▓▓▓  ▓▓▓▓▓▓▓▓           ▓▓   ┃
┃▓ ▓▓ ▓  ▓▓  ▓▓     ▓▓ ▓ ▓▓ ▓▓  ▓┃    ┃▓▓▓▓▓▓  ▓▓▓▓▓▓                  ┃
┃▓▓▓  ▓▓   ▓  ▓  ▓  ▓ ▓  ▓     ▓ ┃    ┃▓▓▓▓▓▓▓            ▓▓▓          ┃
┃▓   ▓▓▓  ▓▓▓▓ ▓▓▓  ▓ ▓▓  ▓  ▓ ▓ ┃    ┃    ▓▓▓       ▓▓▓  ▓▓▓       ▓▓ ┃
┃ ▓  ▓▓▓ ▓     ▓▓ ▓▓ ▓▓       ▓▓▓┃    ┃    ▓▓▓       ▓▓▓▓▓▓▓       ▓▓▓ ┃
┃ ▓ ▓▓   ▓▓     ▓▓▓▓▓    ▓▓▓▓▓▓▓ ┃    ┃ ▓▓▓▓▓  ▓▓     ▓▓▓▓▓▓   ▓▓▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓▓▓▓▓▓  ▓▓ ▓▓ ▓▓ ▓▓  ▓  ▓┃    ┃ ▓▓▓▓   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓▓ ┃
┃ ▓▓▓     ▓▓▓▓▓  ▓▓▓ ▓▓▓  ▓▓ ▓ ▓▓┃    ┃ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓ ┃
┃▓▓▓▓  ▓  ▓  ▓▓▓▓▓▓ ▓▓ ▓▓ ▓▓▓▓▓▓ ┃    ┃ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓ ┃
┃ ▓ ▓▓▓    ▓  ▓ ▓  ▓▓▓     ▓ ▓ ▓ ┃    ┃▓▓▓▓▓▓   ▓▓▓▓░░  ▓▓▓▓    ▓▓▓▓▓▓ ┃
┃▓▓▓▓▓▓ ▓▓▓▓ ▓ ▓  ▓ ▓ ▓   ▓▓▓ ▓▓▓┃    ┃▓▓▓▓▓▓░░▓▓▓▓▓░    ▓▓▓     ▓▓▓▓▓ ┃
┃▓▓ ▓▓ ▓ ▓  ▓ ▓▓ ▓▓ ▓▓ ▓▓▓  ▓ ▓  ┃    ┃▓▓▓▓▓▓░░▓▓▓▓▓       ░░░▓▓  ▓▓▓▓ ┃
┃ ▓▓ ▓ ▓ ▓▓▓▓▓  ▓   ▓   ▓▓  ▓▓ ▓▓┃    ┃▓▓▓▓    ▓▓▓▓▓       ░░░▓▓  ▓▓▓▓ ┃
┃▓▓ ▓  ▓   ▓ ▓ ▓  ▓▓ ▓▓▓ ▓ ▓ ▓ ▓ ┃    ┃ ▓▓▓      ▓▓▓       ░░░░    ▓▓▓ ┃
┃  ▓▓ ▓▓   ▓▓▓ ▓▓▓▓     ▓     ▓▓ ┃    ┃ ▓▓▓▓     ▓▓▓ ▓▓▓▓  ░░░░    ▓▓▓ ┃
┃▓▓ ▓▓ ▓▓       ▓▓   ▓▓▓▓ ▓ ▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓       ▓▓▓▓  ▓▓▓▓    ░░  ┃
┃▓▓▓  ▓  ▓▓▓  ▓▓  ▓▓▓▓▓▓▓     ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓    ░░  ┃
┃▓▓▓ ▓▓▓▓▓▓ ▓▓   ▓  ▓  ▓ ▓  ▓▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓    ▓▓  ┃
┃▓ ▓▓▓   ▓       ▓   ▓▓▓▓▓▓▓ ▓▓▓▓┃    ┃ ▓▓▓▓                ▓▓▓    ▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓ ▓▓▓  ▓  ▓▓▓▓▓  ▓▓▓▓  ▓▓ ▓▓▓┃    ┃   ▓▓▓▓      ▓▓▓    ▓▓▓▓   ▓▓▓▓ ┃
┃   ▓▓▓  ▓▓▓  ▓▓    ▓▓  ▓▓  ▓▓▓  ┃    ┃   ▓▓▓▓▓▓▓▓  ▓▓▓   ▓▓  ▓▓  ▓▓▓▓ ┃
┃▓     ▓ ▓ ▓▓▓▓ ▓ ▓ ▓   ▓▓▓ ▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓  ▓▓  ▓▓▓▓ ┃
┃  ▓  ▓▓▓▓ ▓ ▓  ▓ ▓▓▓▓▓▓  ▓ ▓ ▓  ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓▓▓▓    ▓▓  ▓  ▓▓┃    ┃    ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓ ┃
┃  ▓ ▓ ▓▓▓    ▓       ▓▓▓  ▓▓▓▓ ▓┃    ┃ ▓▓░░▓▓▓▓▓▓▓         ▓▓▓  ▓▓▓▓▓▓┃
┃▓ ▓   ▓▓▓ ▓▓▓        ▓▓▓ ▓▓ ▓▓▓▓┃    ┃ ▓▓  ▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓ ▓ ▓▓▓   ▓▓▓▓▓▓▓ ▓ ▓  ▓ ▓ ┃    ┃ ▓▓░░░▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓  ▓▓ ▓   ▓▓  ▓▓   ▓ ▓▓▓▓▓▓▓▓ ▓┃    ┃   ░░▓▓▓▓▓▓    ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓ ▓  ▓▓▓▓ ▓  ▓      ▓▓▓▓    ▓▓▓┃    ┃   ░▓▓▓▓▓▓     ▓▓   ▓▓▓▓▓    ▓▓ ┃
┃   ▓▓  ▓▓▓ ▓▓ ▓▓▓ ▓ ▓▓    ▓▓   ▓┃    ┃   ▓▓▓▓▓▓▓     ▓▓   ▓▓          ┃
┃ ▓▓ ▓▓▓▓ ▓     ▓▓ ▓ ▓     ▓   ▓ ┃    ┃  ▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓          ┃
┃▓ ▓▓  ▓▓ ▓  ▓▓  ▓▓▓▓▓ ▓  ▓▓  ▓ ▓┃    ┃  ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓   ▓▓     ┃
┃    ▓  ▓▓  ▓▓▓▓ ▓  ▓▓▓▓▓ ▓      ┃    ┃  ▓▓▓▓▓▓▓  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓     ┃
┃ ▓ ▓▓ ▓▓  ▓▓▓▓▓▓  ▓▓ ▓ ▓ ▓▓ ▓ ▓▓┃    ┃  ▓▓▓▓▓▓▓  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓     ┃
┃  ▓▓  ▓▓▓▓ ▓▓▓    ▓▓ ▓  ▓  ▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓▓▓▓   ┃
┃▓▓▓ ▓▓▓  ▓ ▓▓    ▓  ▓   ▓▓ ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓▓   ┃
┃ ▓  ▓▓ ▓▓▓ ▓ ▓ ▓  ▓   ▓▓ ▓▓▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓┃
┃  ▓▓▓   ▓ ▓    ▓▓ ▓▓ ▓▓  ▓  ▓ ▓▓┃    ┃  ░░░░░░░▓▓▓░            ▓▓▓▓▓▓▓┃
┃▓▓  ▓ ▓▓  ▓▓▓▓▓  ▓    ▓  ▓▓ ▓▓ ▓┃    ┃  ░       ▓▓▓▓▓      ▓▓  ▓▓▓▓▓  ┃
┃▓ ▓ ▓ ▓ ▓ ▓▓  ▓      ▓▓▓▓ ▓▓    ┃    ┃          ▓▓  ▓      ▓▓  ▓▓▓▓   ┃
┃ ▓▓▓   ▓ ▓▓   ▓▓  ▓ ▓▓     ▓▓▓  ┃    ┃              ▓▓     ▓▓    ▓▓   ┃
┃   ▓ ▓      ▓▓▓▓▓ ▓   ▓ ▓  ▓  ▓▓┃    ┃            ▓▓▓▓▓▓    ▓▓    ▓▓▓ ┃
┃▓ ▓  ▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓  ▓▓▓▓  ▓▓▓ ┃    ┃            ▓▓▓▓▓▓▓   ▓▓     ▓▓ ┃
┃▓    ▓  ▓   ▓▓▓▓▓▓▓▓▓ ▓▓        ┃    ┃     ▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓        ┃
┃▓ ▓▓▓▓▓▓  ▓▓  ▓ ▓ ▓▓     ▓▓▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓▓▓▓     ▓▓▓    ┃
┃▓▓▓    ▓▓▓▓ ▓ ▓  ▓  ▓▓ ▓▓▓ ▓▓▓▓▓┃    ┃▓▓▓▓  ▓▓▓▓░░▓▓▓  ▓▓▓    ▓▓▓▓▓▓▓ ┃
┃ ▓ ▓  ▓▓▓    ▓▓▓ ▓▓▓   ▓ ▓▓▓ ▓  ┃    ┃       ▓▓    ▓▓   ▓▓    ▓▓▓▓▓▓▓ ┃
┃   ▓   ▓  ▓  ▓▓   ▓ ▓    ▓▓▓ ▓▓ ┃    ┃       ▓▓    ▓▓         ▓▓▓▓▓▓▓ ┃
┃  ▓    ▓▓▓▓▓ ▓ ▓▓   ▓▓  ▓▓ ▓▓▓▓▓┃    ┃       ▓▓▓▓▓ ▓▓     ▓▓  ▓▓▓▓▓▓▓▓┃
┃   ▓▓▓▓▓▓▓▓▓ ▓▓ ▓   ▓▓  ▓ ▓▓▓ ▓▓┃    ┃       ▓▓▓▓▓        ▓▓  ▓▓▓▓▓▓▓▓┃
┃ ▓▓    ▓▓▓▓    ▓▓▓▓▓▓▓  ▓ ▓▓▓ ▓▓┃    ┃       ▓▓▓▓       ░▓▓▓    ▓▓▓▓▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓ ▓▓▓     ▓▓▓  ▓  ▓▓ ▓  ▓▓  ▓┃    ┃    ▓▓▓      ▓▓▓      ▓▓        ┃
┃▓ ▓ ▓▓ ▓   ▓▓▓▓▓ ▓ ▓▓ ▓▓ ▓  ▓ ▓ ┃    ┃   ░▓▓▓    ▓▓▓▓▓   ▓▓▓▓▓        ┃
┃ ▓ ▓▓▓  ▓▓ ▓▓▓▓  ▓  ▓▓▓▓  ▓  ▓▓ ┃    ┃  ░░▓▓     ▓▓▓▓    ▓▓▓▓▓    ▓▓▓ ┃
┃▓ ▓ ▓ ▓  ▓▓     ▓ ▓▓ ▓   ▓▓▓▓▓▓ ┃    ┃ ░░▓▓▓     ▓▓▓▓    ▓▓▓▓     ▓▓▓ ┃
┃▓▓  ▓▓▓  ▓ ▓▓▓▓    ▓▓ ▓      ▓▓▓┃    ┃ ░▓▓▓▓▓    ▓▓▓▓    ▓▓▓▓      ▓▓ ┃
┃ ▓ ▓ ▓▓   ▓  ▓▓    ▓▓▓▓▓▓  ▓  ▓ ┃    ┃ ▓▓▓▓▓▓    ▓▓▓▓    ▓▓▓▓▓        ┃
┃ ▓▓▓▓▓  ▓  ▓▓▓▓     ▓▓▓▓ ▓      ┃    ┃ ▓▓▓▓▓     ▓▓▓▓    ▓▓▓▓▓▓       ┃
┃▓▓▓    ▓   ▓ ▓▓▓ ▓▓ ▓▓▓▓▓▓ ▓ ▓  ┃    ┃▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃▓▓▓▓▓▓ ▓▓▓ ▓▓▓ ▓▓ ▓▓  ▓▓▓  ▓ ▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃ ▓ ▓ ▓▓▓▓▓▓▓   ▓▓ ▓▓ ▓▓   ▓▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓    ▓▓▓  ┃
┃▓  ▓▓▓ ▓   ▓    ▓▓ ▓ ▓▓   ▓ ▓▓  ┃    ┃ ▓▓▓▓▓▓  ▓▓▓    ▓▓▓▓▓▓▓    ▓▓▓  ┃
┃ ▓ ▓▓    ▓▓▓▓▓  ▓ ▓▓▓ ▓▓ ▓  ▓▓ ▓┃    ┃ ▓▓▓▓    ▓▓▓      ▓▓▓▓▓▓▓   ▓▓  ┃
┃ ▓▓ ▓    ▓▓▓   ▓▓  ▓ ▓▓▓▓   ▓   ┃    ┃ ▓▓▓▓    ▓▓▓        ▓▓▓▓▓       ┃
┃  ▓▓▓▓ ▓▓▓   ▓  ▓   ▓ ▓▓▓ ▓  ▓▓ ┃    ┃ ▓▓▓▓                ▓▓▓▓       ┃
┃▓ ▓ ▓   ▓     ▓▓   ▓ ▓  ▓ ▓     ┃    ┃ ▓▓▓         ▓▓▓▓     ▓▓▓▓▓     ┃
┃▓▓▓   ▓   ▓▓▓▓▓▓▓▓ ▓  ▓ ▓▓▓ ▓▓ ▓┃    ┃▓▓▓▓      ▓▓▓▓▓▓▓     ▓▓▓▓▓▓    ┃
┃▓▓▓▓   ▓▓▓▓  ▓▓▓▓ ▓    ▓ ▓▓▓ ▓  ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓   ┃
┃▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓ ▓    ▓ ▓▓▓▓▓ ▓ ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓   ┃
┃ ▓▓      ▓▓  ▓▓▓▓▓▓▓▓  ▓ ▓ ▓   ▓┃    ┃ ▓▓▓     ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃   ▓▓▓   ▓   ▓▓▓ ▓ ▓▓▓▓▓▓▓ ▓▓  ▓┃    ┃  ▓▓     ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓ ▓  ▓▓ ▓▓  ▓  ▓ ▓▓▓   ▓▓▓▓▓▓▓▓┃    ┃  ░░▓▓▓▓▓▓▓       ▓▓▓   ▓▓▓▓▓▓▓ ┃
┃  ▓ ▓ ▓▓▓ ▓▓▓ ▓    ▓     ▓▓   ▓ ┃    ┃  ░▓▓▓▓▓▓▓▓▓▓     ▓▓     ▓▓▓▓▓▓▓┃
┃▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓  ▓▓▓ ▓    ▓▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓     ▓▓▓▓▓▓▓┃
┃▓▓  ▓▓  ▓  ▓            ▓▓▓▓ ▓ ▓┃    ┃▓▓▓     ▓▓▓▓             ▓▓▓▓▓▓▓┃
┃▓▓▓     ▓▓▓▓ ▓▓ ▓ ▓   ▓▓ ▓ ▓  ▓▓┃    ┃▓▓▓     ▓▓▓▓ ▓▓       ▓▓▓▓▓▓▓▓▓▓┃
┃▓▓   ▓ ▓▓▓▓▓ ▓▓ ▓     ▓▓▓▓ ▓▓▓  ┃    ┃▓▓▓   ▓▓▓▓▓▓ ▓▓       ▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓▓▓ ▓ ▓ ▓  ▓▓  ▓▓▓ ▓▓ ▓▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓  ▓ ▓ ▓▓▓▓ ▓▓▓     ▓▓▓ ▓▓▓▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓▓   ▓    ▓▓▓      ▓ ▓    ▓ ▓┃    ┃▓▓▓▓▓  ▓▓▓   ▓▓▓          ▓▓▓▓▓ ┃
┃   ▓ ▓▓▓▓▓ ▓▓ ▓▓▓▓        ▓▓▓▓▓ ┃    ┃       ▓▓    ▓▓▓          ▓▓▓▓▓ ┃
┃  ▓    ▓   ▓   ▓ ▓ ▓ ▓▓   ▓▓  ▓ ┃    ┃       ▓▓           ▓▓▓   ▓▓▓▓▓ ┃
┃ ▓  ▓  ▓▓    ▓  ▓ ▓▓▓▓▓   ▓▓▓▓▓ ┃    ┃                    ▓▓▓   ▓▓▓▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓    ▓        ▓   ▓▓▓▓  ▓▓    ┃    ┃▓▓                  ▓▓▓▓        ┃
┃▓     ▓▓▓▓▓   ▓▓   ▓▓ ▓▓▓▓▓     ┃    ┃▓▓    ▓▓▓▓▓        ▓▓▓▓▓▓▓      ┃
┃▓▓▓▓▓▓▓ ▓ ▓▓▓▓▓  ▓▓▓  ▓▓  ▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓     ┃
┃▓ ▓ ▓ ▓  ▓ ▓▓   ▓▓ ▓▓▓ ▓ ▓ ▓▓  ▓┃    ┃ ▓▓▓▓▓▓  ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃  ▓ ▓▓▓▓ ▓▓ ▓ ▓▓ ▓     ▓  ▓▓▓ ▓▓┃    ┃  ▓▓▓▓▓  ▓▓▓▓             ▓▓▓   ┃
┃ ▓▓▓    ▓   ▓   ▓▓▓ ▓   ▓▓  ▓ ▓ ┃    ┃                          ▓▓▓   ┃
┃     ▓▓  ▓▓  ▓▓  ▓ ▓▓ ▓  ▓ ▓▓  ▓┃    ┃     ▓▓            ▓▓     ░░    ┃
┃ ▓▓▓ ▓▓▓  ▓ ▓▓ ▓  ▓▓ ▓ ▓  ▓  ▓  ┃    ┃ ▓▓  ▓▓      ▓▓    ▓▓▓    ░░    ┃
┃▓▓▓   ▓ ▓▓    ▓▓▓    ▓▓▓▓▓ ▓  ▓ ┃    ┃ ▓▓  ▓▓      ▓▓▓     ▓▓▓▓▓░     ┃
┃ ▓ ▓ ▓▓  ▓  ▓▓▓ ▓  ▓▓   ▓▓▓ ▓▓  ┃    ┃     ▓▓      ▓▓▓        ▓▓      ┃
┃▓     ▓   ▓▓ ▓ ▓ ▓   ▓   ▓ ▓▓   ┃    ┃     ▓▓   ▓▓▓▓▓▓                ┃
┃     ▓▓▓ ▓▓ ▓▓▓   ▓▓▓▓ ▓  ▓   ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓┃
┃    ▓▓ ▓▓   ▓▓▓ ▓▓▓▓ ▓▓ ▓ ▓   ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓┃
┃▓   ▓ ▓ ▓▓▓▓ ▓  ▓ ▓▓ ▓▓▓▓ ▓ ▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃    ▓ ▓   ▓▓ ▓   ▓  ▓▓   ▓▓▓▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓  ▓ ▓▓▓ ▓▓  ▓ ▓▓▓▓▓▓ ▓▓▓▓ ▓▓ ▓┃    ┃▓▓  ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓  ▓▓  ▓▓ ▓    ▓▓ ▓ ▓▓ ▓▓ ▓▓ ▓ ┃    ┃▓▓              ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓ ▓     ▓▓  ▓▓▓ ▓  ▓▓ ▓ ▓▓▓▓┃    ┃            ▓▓  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓┃
┃      ▓ ▓   ▓▓▓ ▓▓    ▓   ▓ ▓▓▓▓┃    ┃            ▓▓▓▓▓▓▓    ▓▓  ▓▓▓▓▓┃
┃▓▓   ▓ ▓ ▓ ▓▓▓▓   ▓   ▓▓▓  ▓▓   ┃    ┃           ▓▓▓▓▓▓▓▓    ▓▓  ▓▓▓  ┃
┃   ▓   ▓▓▓ ▓▓ ▓▓▓▓   ▓  ▓▓ ▓▓▓▓ ┃    ┃           ▓▓▓▓▓▓▓▓        ▓▓▓  ┃
┃ ▓▓▓▓ ▓ ▓  ▓▓▓ ▓▓ ▓▓▓ ▓   ▓ ▓   ┃    ┃ ▓▓▓░░▓▓   ▓▓▓▓▓▓▓▓▓▓      ▓▓▓  ┃
┃▓▓▓▓ ▓▓▓  ▓▓ ▓▓  ▓▓▓    ▓ ▓ ▓▓▓▓┃    ┃ ▓▓▓░░▓▓   ▓▓▓▓▓  ▓▓▓▓    ▓▓▓▓▓ ┃
┃ ▓    ▓▓  ▓   ▓▓  ▓▓▓▓ ▓▓▓ ▓▓  ▓┃    ┃ ▓▓  ░▓▓          ▓▓▓▓    ▓▓▓▓▓ ┃
┃ ▓▓  ▓▓▓    ▓ ▓      ▓▓  ▓ ▓▓▓ ▓┃    ┃ ▓▓  ░▓▓           ▓▓▓     ▓▓▓▓ ┃
┃ ▓▓ ▓ ▓▓▓  ▓   ▓  ▓▓▓▓       ▓▓ ┃    ┃ ▓▓░░░▓▓            ▓▓       ▓▓ ┃
┃▓▓▓▓ ▓▓  ▓▓▓  ▓ ▓   ▓▓   ▓ ▓  ▓▓┃    ┃▓▓▓░░    ▓▓▓        ▓▓       ▓▓ ┃
┃▓▓  ▓   ▓▓▓    ▓▓ ▓  ▓▓ ▓▓   ▓  ┃    ┃▓▓       ▓▓▓    ▓▓  ▓▓▓▓     ▓▓ ┃
┃▓      ▓  ▓▓    ▓▓▓▓▓▓▓▓ ▓  ▓▓▓ ┃    ┃          ▓▓    ▓▓▓▓▓▓▓▓▓    ▓▓ ┃
┃    ▓▓     ▓  ▓  ▓▓▓▓▓▓      ▓▓ ┃    ┃                ▓▓▓▓▓▓▓▓▓   ▓▓▓ ┃
┃▓ ▓▓   ▓ ▓▓ ▓▓ ▓▓▓   ▓▓▓ ▓▓▓▓▓▓ ┃    ┃  ▓▓            ▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓     ▓       ▓   ▓ ▓▓▓▓  ▓▓ ┃    ┃  ▓▓                  ▓▓▓▓▓  ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃          ▓  ▓ ▓▓▓    ▓ ▓  ▓    ┃    ┃               ▓▓               ┃
┃  ▓▓▓ ▓ ▓ ▓▓▓▓ ▓▓  ▓▓▓  ▓▓   ▓  ┃    ┃  ▓▓▓     ▓▓▓▓▓▓▓  ▓▓▓          ┃
┃▓▓▓▓▓ ▓▓ ▓▓▓  ▓▓   ▓▓▓   ▓▓  ▓  ┃    ┃▓▓▓▓▓▓▓░░▓▓▓▓      ▓▓▓          ┃
┃▓▓▓▓▓▓▓ ▓   ▓    ▓ ▓▓▓▓    ▓▓   ┃    ┃▓▓▓▓▓▓▓░░▓▓▓       ▓▓▓▓    ▓▓▓  ┃
┃   ▓▓    ▓▓▓  ▓▓   ▓▓ ▓▓   ▓▓▓▓ ┃    ┃▓▓▓▓▓    ▓▓        ▓▓▓▓    ▓▓▓▓ ┃
┃▓▓▓▓  ▓  ▓▓ ▓  ▓▓▓▓▓▓▓ ▓ ▓▓▓ ▓▓▓┃    ┃▓▓▓▓▓    ▓▓    ▓▓▓▓▓▓▓▓▓   ▓▓▓▓ ┃
┃▓ ▓ ▓▓  ▓ ▓    ▓  ▓▓▓▓  ▓      ▓┃    ┃▓▓▓▓     ░░    ▓▓▓▓▓▓▓▓▓        ┃
┃▓▓▓▓     ▓  ▓▓▓▓▓▓ ▓▓▓▓▓ ▓   ▓  ┃    ┃▓▓▓▓     ░░   ▓▓▓▓▓▓▓▓▓▓        ┃
┃▓▓ ▓ ▓▓  ▓▓▓ ▓  ▓▓▓  ▓ ▓  ▓▓  ▓ ┃    ┃▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓░        ┃
┃▓ ▓▓   ▓  ▓▓▓ ▓▓ ▓▓ ▓ ▓    ▓ ▓▓ ┃    ┃▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓░░  ▓▓▓▓▓ ┃
┃▓  ▓▓ ▓ ▓ ▓▓▓▓▓  ▓  ▓ ▓▓▓▓▓▓ ▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ░▓▓▓▓▓▓▓▓ ┃
┃▓▓ ▓▓▓ ▓ ▓▓ ▓ ▓     ▓   ▓ ▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓░ ┃
┃ ▓▓▓  ▓▓▓ ▓▓▓   ▓▓▓ ▓  ▓▓  ▓ ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓      ▓    ░░ ┃
┃▓▓▓ ▓▓▓ ▓▓ ▓▓▓  ▓   ▓▓▓  ▓  ▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ▓▓▓ ▓    ░░ ┃
┃▓   ▓ ▓▓ ▓      ▓▓ ▓▓▓▓ ▓▓   ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓      ▓▓  ▓▓▓ ▓▓   ▓▓▓┃
┃  ▓▓ ▓▓ ▓▓    ▓▓▓  ▓    ▓▓   ▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓   ▓▓   ▓▓▓┃
┃ ▓▓▓▓▓▓ ▓▓▓▓▓ ▓▓ ▓▓ ▓   ▓ ▓▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓   ▓▓ ┃
┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓ ▓▓ ▓▓  ▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓ ┃
┃▓▓▓▓  ▓ ▓▓  ▓▓▓▓▓▓ ▓▓    ▓   ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓        ▓▓ ┃
┃▓▓ ▓▓▓ ▓▓     ▓▓ ▓ ▓▓▓       ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓        ▓▓ ┃
┃▓▓▓  ▓ ▓ ▓▓▓ ▓  ▓ ▓▓     ▓ ▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ▓▓ ┃
┃ ▓ ▓  ▓▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓  ▓▓▓ ▓ ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓▓▓┃
┃ ▓▓▓▓▓▓ ▓▓▓  ▓ ▓ ▓▓▓       ▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓      ▓▓▓       ▓▓▓▓▓┃
┃▓     ▓   ▓       ▓▓ ▓  ▓ ▓▓  ▓▓┃    ┃ ▓▓       ▓      ▓▓▓       ▓▓▓▓▓┃
┃▓▓ ▓   ▓  ▓▓  ▓ ▓▓   ▓▓   ▓ ▓▓▓▓┃    ┃▓▓▓       ▓     ▓▓▓  ▓▓    ▓▓▓▓▓┃
┃▓▓▓▓▓  ▓ ▓▓    ▓▓▓▓  ▓▓ ▓    ▓  ┃    ┃▓▓▓▓▓    ▓▓▓   ▓▓▓▓  ▓▓    ░░   ┃
┃▓▓▓ ▓ ▓  ▓▓▓  ▓ ▓▓▓ ▓   ▓▓▓ ▓   ┃    ┃▓▓▓▓▓    ▓▓▓   ▓▓▓▓        ░░   ┃
┃▓▓▓▓▓ ▓    ▓▓  ▓▓  ▓▓▓ ▓   ▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓        ▓▓▓         ▓▓   ┃
┃▓▓▓  ▓▓    ▓   ▓ ▓      ▓▓ ▓ ▓  ┃    ┃▓▓▓▓▓▓▓                 ▓▓▓▓▓   ┃
┃▓▓  ▓▓  ▓    ▓▓         ▓ ▓▓▓   ┃    ┃▓▓▓▓▓▓       ▓▓         ▓▓▓▓▓   ┃
┃▓▓▓ ▓▓  ▓  ▓▓▓▓ ▓  ▓▓ ▓ ▓▓ ▓▓  ▓┃    ┃▓▓  ▓▓     ▓▓▓▓         ▓▓▓▓▓   ┃
┃▓   ▓  ▓   ▓▓  ▓▓    ▓ ▓ ▓▓▓▓▓▓▓┃    ┃           ▓▓           ▓▓▓▓▓   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓      ▓▓  ▓ ▓▓ ▓▓▓   ▓▓▓  ▓▓┃    ┃                ▓▓▓▓▓         ▓▓┃
┃ ▓ ▓▓▓ ▓ ▓ ▓  ▓▓ ▓▓▓▓   ▓  ▓▓▓▓▓┃    ┃              ▓▓▓▓▓▓▓        ░▓▓┃
┃▓▓ ▓  ▓     ▓▓ ▓ ▓▓   ▓▓    ▓  ▓┃    ┃              ▓▓▓▓▓▓   ▓▓     ▓▓┃
┃▓    ▓▓ ▓  ▓   ▓▓▓▓ ▓  ▓▓▓▓   ▓▓┃    ┃               ▓▓▓▓▓  ▓▓▓▓▓     ┃
┃ ▓▓      ▓ ▓   ▓  ▓▓ ▓▓▓ ▓▓  ▓  ┃    ┃               ▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃   ▓▓▓▓▓ ▓   ▓▓ ▓▓▓▓▓▓▓▓▓ ▓▓ ▓ ▓┃    ┃     ▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃  ▓  ▓   ▓▓  ▓ ▓▓ ▓▓▓▓ ▓   ▓ ▓  ┃    ┃     ▓▓  ▓▓    ▓▓▓▓▓▓▓▓▓        ┃
┃ ▓ ▓ ▓▓   ▓    ▓ ▓ ▓   ▓    ▓▓ ▓┃    ┃    ░▓▓  ▓▓      ▓▓▓▓▓▓▓     ▓▓ ┃
┃▓▓ ▓▓ ▓▓▓▓▓   ▓    ▓ ▓▓▓▓▓ ▓  ▓▓┃    ┃     ▓▓▓▓▓▓         ▓▓▓▓▓▓   ▓▓▓┃
┃  ▓    ▓▓ ▓▓  ▓  ▓  ▓▓   ▓ ▓ ▓▓ ┃    ┃       ▓▓▓▓▓        ▓▓  ▓▓▓  ▓▓▓┃
┃▓ ▓    ▓   ▓ ▓▓▓▓ ▓  ▓  ▓▓▓  ▓ ▓┃    ┃       ▓▓▓▓▓  ▓▓    ▓▓   ▓▓  ▓▓ ┃
┃▓▓   ▓▓ ▓ ▓▓  ▓▓ ▓  ▓▓   ▓▓ ▓▓  ┃    ┃       ░░▓▓▓▓▓▓▓░░░▓▓▓   ▓▓     ┃
┃▓ ▓▓ ▓   ▓  ▓▓▓▓ ▓▓▓▓  ▓ ▓▓     ┃    ┃    ░░░░░░▓▓▓▓▓▓░░░▓▓    ▓▓     ┃
┃  ▓ ▓ ▓ ▓▓▓ ▓▓▓    ▓▓ ▓▓ ▓▓▓▓▓ ▓┃    ┃     ░░░░░░▓▓▓▓    ▓▓  ▓▓▓▓▓▓▓  ┃
┃▓▓   ▓▓▓ ▓ ▓▓▓   ▓     ▓▓▓▓ ▓▓  ┃    ┃          ░░▓▓        ▓▓▓▓▓▓▓▓  ┃
┃  ▓▓      ▓ ▓  ▓   ▓▓▓▓ ▓  ▓ ▓▓ ┃    ┃            ▓▓        ▓▓▓▓▓▓▓▓  ┃
┃  ▓ ▓▓▓ ▓    ▓▓▓▓  ▓  ▓ ▓▓ ▓▓  ▓┃    ┃  ▓▓▓▓      ▓▓▓▓        ▓▓▓▓▓   ┃
┃▓▓▓▓▓   ▓▓ ▓ ▓▓ ▓ ▓ ▓    ▓▓  ▓  ┃    ┃▓▓▓▓▓▓      ▓▓▓▓        ▓▓▓▓▓   ┃
┃▓▓ ▓ ▓ ▓  ▓ ▓▓   ▓▓  ▓▓▓ ▓▓▓ ▓▓ ┃    ┃▓▓▓▓▓▓                   ▓▓▓▓   ┃
┃▓ ▓ ▓▓▓  ▓     ▓ ▓  ▓   ▓▓▓▓▓  ▓┃    ┃▓▓▓▓▓▓▓                  ▓▓▓▓   ┃
┃▓ ▓ ▓ ▓▓ ▓      ▓ ▓▓  ▓  ▓  ▓ ▓ ┃    ┃ ▓▓▓▓▓▓                         ┃
┃ ▓▓▓  ▓ ▓  ▓▓▓  ▓    ▓    ▓ ▓ ▓ ┃    ┃ ▓▓▓▓                           ┃
┃ ▓▓ ▓▓   ▓▓   ▓  ▓  ▓▓▓ ▓     ▓ ┃    ┃ ▓▓▓▓    ▓▓                     ┃
┃▓   ▓  ▓ ▓▓  ▓ ▓   ▓▓    ▓ ▓▓▓▓▓┃    ┃         ▓▓        ▓▓       ░   ┃
┃▓ ▓  ▓▓   ▓ ▓▓   ▓ ▓  ▓▓ ▓  ▓   ┃    ┃            ▓▓     ▓▓       ▓   ┃
┃▓ ▓▓▓ ▓  ▓  ▓  ▓▓  ▓▓  ▓▓ ▓ ▓  ▓┃    ┃    ▓▓      ▓▓           ▓▓▓▓   ┃
┃ ▓  ▓▓ ▓▓  ▓▓▓▓  ▓▓       ▓▓▓▓  ┃    ┃    ▓▓     ▓▓▓          ▓▓▓▓▓   ┃
┃▓▓  ▓▓   ▓ ▓▓   ▓  ▓   ▓▓▓▓▓    ┃    ┃    ▓▓     ▓▓           ▓▓▓▓▓   ┃
┃  ▓   ▓    ▓  ▓▓  ▓▓ ▓  ▓▓▓▓ ▓ ▓┃    ┃    ▓▓     ▓  ▓▓▓▓▓▓   ▓▓▓▓▓▓▓  ┃
┃ ▓ ▓▓▓▓   ▓▓  ▓▓▓▓  ▓ ▓▓▓  ▓▓ ▓▓┃    ┃    ▓▓▓   ▓▓  ▓▓▓▓▓▓   ▓▓  ▓▓▓  ┃
┃  ▓ ▓▓  ▓▓▓▓▓▓▓ ▓ ▓▓ ▓  ▓   ▓▓  ┃    ┃    ▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓  ┃
┃  ▓  ▓▓ ▓▓ ▓▓▓    ▓  ▓   ▓▓▓▓▓▓ ┃    ┃        ▓▓▓▓▓▓             ▓▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓   ▓▓▓ ▓▓  ▓ ▓▓▓ ▓ ▓        ▓  ┃    ┃      ▓▓▓                       ┃
┃   ▓  ▓▓▓  ▓    ▓  ▓ ▓▓▓▓▓ ▓▓ ▓ ┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓     ┃
┃      ▓▓▓▓▓ ▓   ▓▓   ▓▓▓▓▓ ▓  ▓ ┃    ┃      ▓▓▓▓           ▓▓▓▓▓▓▓    ┃
┃▓▓ ▓▓  ▓▓  ▓ ▓▓▓    ▓  ▓▓▓▓▓    ┃    ┃       ▓▓▓    ▓▓▓    ▓▓▓▓▓▓▓    ┃
┃ ▓     ▓ ▓     ▓▓▓▓▓ ▓  ▓▓ ▓  ▓▓┃    ┃▓▓            ▓▓▓▓▓  ▓▓▓▓▓▓     ┃
┃▓▓        ▓▓▓ ▓▓ ▓▓  ▓▓ ▓ ▓     ┃    ┃▓▓             ▓▓▓▓  ▓▓▓▓▓      ┃
┃▓ ▓ ▓ ▓ ▓▓       ▓▓    ▓▓   ▓▓▓ ┃    ┃▓▓▓▓           ▓▓▓▓  ▓▓▓▓▓      ┃
┃▓ ▓▓▓▓     ▓▓ ▓▓▓  ▓▓▓▓ ▓ ▓▓    ┃    ┃  ▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓▓  ▓ ▓  ▓▓▓▓▓▓▓▓▓▓ ▓▓▓▓  ▓▓  ┃    ┃  ▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░    ┃
┃ ▓   ▓   ▓  ▓   ▓▓▓▓ ▓▓   ▓▓ ▓ ▓┃    ┃            ▓  ▓▓▓▓▓▓▓▓   ░░░   ┃
┃▓▓ ▓ ▓▓ ▓ ▓ ▓  ▓▓▓▓ ▓ ▓   ▓ ▓ ▓▓┃    ┃ ▓▓  ░      ▓  ▓▓▓▓▓▓▓▓   ░░░▓▓▓┃
┃ ▓▓▓ ▓ ▓▓   ▓▓ ▓ ▓  ▓▓ ▓▓▓ ▓  ▓▓┃    ┃ ▓▓▓▓▓      ▓▓▓▓▓  ▓▓▓▓░░░░░▓▓▓▓┃
┃▓▓ ▓▓ ▓ ▓   ▓▓▓▓▓  ▓▓ ▓ ▓  ▓▓ ▓▓┃    ┃ ▓▓▓▓▓      ▓▓▓▓   ▓▓▓▓░░░░▓▓▓▓▓┃
┃ ▓▓▓ ▓▓▓  ▓ ▓▓     ▓ ▓ ▓ ▓▓  ▓  ┃    ┃▓▓▓▓▓▓      ▓▓     ▓▓▓▓░░▓▓▓▓▓▓ ┃
┃▓  ▓▓▓    ▓▓ ▓ ▓ ▓ ▓ ▓▓ ▓▓▓▓▓▓▓ ┃    ┃▓▓▓▓▓▓      ▓      ▓▓▓▓░░▓▓▓▓▓▓ ┃
┃▓▓▓  ▓  ▓▓  ▓  ▓  ▓▓ ▓▓▓    ▓▓▓ ┃    ┃▓▓       ▓▓▓▓      ▓▓▓▓░▓▓▓▓▓▓▓ ┃
┃▓   ▓ ▓ ▓ ▓▓▓  ▓▓  ▓ ▓▓  ▓▓▓ ▓ ▓┃    ┃▓       ▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓  ▓▓▓  ▓▓ ▓▓▓▓▓  ▓ ▓▓ ▓▓▓   ▓▓ ┃    ┃▓       ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓  ▓▓▓┃
┃▓▓     ▓▓▓ ▓▓▓ ▓ ▓    ▓ ▓ ▓▓  ▓▓┃    ┃▓▓      ▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓  ▓▓▓┃
┃▓▓▓ ▓ ▓ ▓ ▓▓ ▓  ▓▓▓   ▓  ▓▓  ▓ ▓┃    ┃▓▓ ░     ▓▓▓▓  ▓▓▓    ▓▓▓▓▓   ▓▓┃
┃ ▓ ▓ ▓     ▓   ▓▓▓ ▓▓▓▓▓▓▓    ▓▓┃    ┃   ░░     ▓▓    ▓▓  ▓▓▓▓▓▓▓   ▓▓┃
┃ ▓▓   ▓   ▓▓    ▓▓   ▓▓▓▓▓▓ ▓ ▓ ┃    ┃   ░░░    ▓▓    ▓▓  ▓▓▓▓▓▓▓     ┃
┃▓  ▓▓▓ ▓▓ ▓ ▓  ▓▓  ▓▓ ▓ ▓ ▓ ▓  ▓┃    ┃   ▓▓▓▓   ▓▓    ▓▓  ▓▓▓▓▓▓▓     ┃
┃▓ ▓ ▓▓▓  ▓▓▓ ▓▓  ▓▓ ▓▓   ▓ ▓▓ ▓▓┃    ┃   ▓▓▓▓░░░▓▓    ▓▓▓▓▓   ▓▓▓▓▓   ┃
┃   ▓▓ ▓ ▓  ▓ ▓  ▓▓ ▓▓  ▓ ▓▓ ▓  ▓┃    ┃   ▓▓▓▓░░▓▓▓    ▓▓▓▓▓   ▓▓▓▓▓   ┃
┃▓  ▓▓  ▓ ▓▓▓  ▓ ▓   ▓  ▓▓ ▓▓▓   ┃    ┃   ▓▓    ▓▓▓    ▓▓▓▓▓  ▓▓▓▓▓▓   ┃
┃▓       ▓  ▓▓   ▓▓▓▓▓▓▓ ▓    ▓▓▓┃    ┃         ▓▓▓▓   ▓▓▓▓▓▓▓▓▓       ┃
┃ ▓ ▓  ▓  ▓ ▓▓▓▓   ▓▓▓ ▓ ▓     ▓ ┃    ┃         ▓▓▓▓▓   ▓▓▓▓▓  ▓       ┃
┃▓ ▓▓ ▓▓  ▓▓ ▓▓   ▓ ▓▓▓  ▓▓▓ ▓  ▓┃    ┃         ▓▓▓▓▓    ▓▓▓   ▓▓▓     ┃
┃      ▓▓▓▓▓▓▓ ▓ ▓   ▓  ▓▓▓ ▓  ▓ ┃    ┃      ▓▓▓▓▓▓▓▓     ▓▓   ▓▓▓     ┃
┃      ▓▓▓▓▓▓▓ ▓▓  ▓▓▓    ▓▓ ▓▓▓ ┃    ┃      ▓▓▓▓▓▓▓▓     ▓▓    ▓▓     ┃
┃▓    ▓ ▓ ▓▓  ▓  ▓      ▓  ▓   ▓ ┃    ┃       ▓▓▓▓                     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓   ▓    ▓ ▓▓▓▓ ▓  ▓ ▓▓▓▓  ┃    ┃                  ▓▓      ▓▓▓   ┃
┃    ▓ ▓ ▓ ▓ ▓ ▓  ▓ ▓ ▓▓ ▓ ▓▓▓   ┃    ┃                  ▓▓▓▓▓   ▓▓▓   ┃
┃ ▓  ▓   ▓     ▓    ▓▓  ▓    ▓  ▓┃    ┃                   ▓▓▓▓▓        ┃
┃ ▓ ▓▓▓ ▓ ▓     ▓  ▓ ▓▓▓▓▓▓▓   ▓▓┃    ┃                   ▓▓▓▓▓▓▓▓   ▓▓┃
┃  ▓  ▓    ▓ ▓▓  ▓  ▓▓▓▓ ▓▓▓▓ ▓▓ ┃    ┃    ░      ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃    ▓ ▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓ ▓▓┃    ┃    ░░    ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓ ▓ ▓   ▓   ▓  ▓  ▓ ▓ ▓ ▓▓▓  ┃    ┃ ▓▓░░░     ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓   ▓   ▓▓▓▓▓    ▓▓▓  ▓ ▓▓▓▓┃    ┃ ▓▓░░░     ▓▓▓▓▓     ▓▓    ▓▓▓▓▓┃
┃    ▓▓▓    ▓      ▓▓▓      ▓▓  ▓┃    ┃    ▓▓     ░░░     ▓▓▓▓    ▓▓▓▓▓┃
┃▓   ▓▓ ▓ ▓▓ ▓▓ ▓    ▓▓ ▓▓▓ ▓ ▓▓▓┃    ┃    ▓▓     ░░░     ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓ ▓ ▓▓  ▓▓ ▓  ▓  ▓ ▓▓▓▓▓ ▓▓▓  ┃    ┃           ░▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓ ▓  ▓   ▓   ▓▓▓  ▓▓ ▓▓▓ ▓▓▓ ▓ ▓┃    ┃         ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓▓ ▓ ▓▓ ▓▓  ▓   ▓▓  ▓▓  ▓▓▓   ┃    ┃         ▓▓▓▓▓▓   ▓▓  ▓▓▓▓▓▓▓   ┃
┃▓ ▓  ▓▓ ▓ ▓▓ ▓▓ ▓ ▓▓   ▓▓▓▓▓   ▓┃    ┃          ▓▓▓▓▓   ▓▓  ▓▓▓▓▓▓    ┃
┃▓▓     ▓    ▓  ▓  ▓▓▓▓ ▓▓ ▓ ▓  ▓┃    ┃                  ▓▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓▓▓▓   ▓▓ ▓  ▓     ▓▓ ▓ ▓  ▓▓▓┃    ┃ ▓▓▓▓                 ▓▓▓    ▓▓▓┃
┃ ▓ ▓▓  ▓▓  ▓   ▓        ▓    ▓▓▓┃    ┃▓▓▓▓▓                        ▓▓▓┃
┃▓▓▓    ▓ ▓ ▓▓▓ ▓▓▓ ▓ ▓ ▓▓▓▓   ▓ ┃    ┃▓▓▓▓     ▓▓▓▓▓▓▓▓▓              ┃
┃▓▓ ▓   ▓  ▓▓ ▓▓▓▓▓ ▓▓▓     ▓  ▓ ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓          ┃
┃▓▓ ▓▓ ▓▓▓▓ ▓  ▓ ▓▓▓▓ ▓▓▓▓ ▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓          ┃
┃  ▓▓▓▓▓▓ ▓▓▓▓  ▓ ▓  ▓    ▓  ▓▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓  ▓▓▓▓  ▓▓          ┃
┃     ▓▓ ▓     ▓▓▓   ▓▓▓  ▓▓▓ ▓ ▓┃    ┃     ▓▓▓      ▓▓▓▓  ▓▓   ▓▓▓▓▓▓ ┃
┃▓▓▓   ▓ ▓ ▓ ▓▓ ▓▓▓▓▓   ▓ ▓▓ ▓▓▓▓┃    ┃     ▓░▓    ▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓▓ ┃
┃   ▓▓  ▓  ▓▓ ▓▓▓  ▓▓▓ ▓ ▓▓▓▓▓  ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓░░▓▓▓▓▓▓ ┃
┃▓▓ ▓▓ ▓ ▓▓ ▓▓ ▓▓  ▓ ▓▓▓  ▓  ▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓  ┃
┃ ▓▓▓ ▓ ▓▓▓     ▓ ▓  ▓  ▓ ▓▓ ▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓      ▓▓▓▓▓  ┃
┃▓▓▓▓ ▓▓▓▓▓  ▓ ▓▓▓ ▓   ▓ ▓  ▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓     ▓▓▓▓▓▓  ┃
┃▓▓▓    ▓▓   ▓  ▓ ▓▓▓▓   ▓ ▓▓ ▓▓▓┃    ┃▓▓▓   ▓▓▓      ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓┃
┃ ▓    ▓▓▓ ▓▓   ▓▓▓▓▓▓▓▓▓▓ ▓▓▓ ▓▓┃    ┃░░     ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓    ▓ ▓  ▓ ▓▓   ▓▓ ▓    ▓ ┃    ┃░░        ▓▓▓   ▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓  ▓  ▓▓▓▓ ▓   ▓▓ ▓▓▓▓▓▓ ▓   ▓ ┃    ┃▓▓        ▓▓▓    ▓▓▓▓▓▓▓▓       ┃
┃▓▓   ▓ ▓  ▓▓▓▓▓   ▓▓ ▓▓▓   ▓    ┃    ┃▓▓        ▓▓▓      ▓▓▓▓▓        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓   ▓▓ ▓▓▓  ▓▓▓  ▓▓    ▓  ▓▓ ▓┃    ┃      ▓▓       ▓▓               ┃
┃▓ ▓ ▓▓▓▓  ▓  ▓ ▓▓▓▓ ▓ ▓      ▓  ┃    ┃      ▓▓ ▓▓    ▓▓               ┃
┃▓ ▓      ▓▓ ▓▓      ▓ ▓  ▓▓  ▓  ┃    ┃▓▓▓      ▓▓        ▓▓▓▓         ┃
┃▓▓ ▓  ▓▓▓▓▓▓    ▓ ▓▓▓▓▓  ▓   ▓  ┃    ┃▓▓▓   ▓▓▓▓▓        ▓▓▓▓         ┃
┃▓▓▓▓  ▓▓ ▓▓ ▓  ▓ ▓ ▓▓ ▓▓▓▓ ▓▓▓ ▓┃    ┃▓▓▓   ▓▓▓▓▓░      ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓   ▓  ▓  ▓ ▓  ▓▓  ▓   ▓ ▓▓▓▓ ┃    ┃▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓  ▓ ▓ ▓  ▓▓▓▓▓▓ ▓▓▓ ▓▓ ▓▓▓▓▓▓┃    ┃▓▓          ▓▓▓▓▓▓▓▓▓  ░░▓▓▓▓▓▓ ┃
┃▓  ▓   ▓  ▓▓ ▓  ▓▓▓▓▓  ▓     ▓  ┃    ┃▓▓        ▓▓▓▓  ▓▓▓▓▓  ░▓▓▓▓▓▓▓ ┃
┃▓▓▓   ▓▓▓ ▓▓▓▓  ▓▓ ▓    ▓▓ ▓▓ ▓▓┃    ┃▓▓▓▓    ▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓▓▓▓ ┃
┃  ▓▓   ▓ ▓▓ ▓▓▓▓  ▓ ▓  ▓▓▓▓▓▓▓▓ ┃    ┃ ▓▓▓    ▓▓▓▓▓▓░░▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓▓ ▓▓ ▓ ▓ ▓ ▓▓▓  ▓▓▓ ▓▓▓▓▓▓┃    ┃  ▓▓▓▓░░▓▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃    ▓▓ ▓▓▓ ▓  ▓  ▓  ▓ ▓▓  ▓ ▓ ▓▓┃    ┃    ▓▓░░▓▓   ░░      ▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓      ▓   ▓ ▓ ▓   ▓▓▓▓▓▓▓ ▓▓ ┃    ┃        ▓▓   ░░      ▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓▓   ▓▓   ▓▓  ▓ ▓ ▓▓▓ ▓   ▓▓▓┃    ┃  ▓▓▓   ▓▓   ▓▓      ▓▓▓▓▓   ▓▓▓┃
┃  ▓▓▓ ▓ ▓▓▓  ▓▓ ▓ ▓   ▓ ▓ ▓ ▓  ▓┃    ┃  ▓▓▓   ▓▓▓  ▓▓      ▓▓▓▓▓   ▓▓▓┃
┃▓▓▓       ▓▓▓   ▓▓▓ ▓▓▓ ▓▓  ▓ ▓ ┃    ┃▓▓▓▓▓     ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓┃
┃▓▓▓▓▓▓    ▓▓ ▓  ▓ ▓▓▓▓  ▓▓ ▓▓▓▓▓┃    ┃▓▓▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓┃
┃ ▓ ▓ ▓▓   ▓▓ ▓▓ ▓▓▓▓▓ ▓▓      ▓▓┃    ┃▓▓▓▓▓▓    ▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓     ▓▓┃
┃▓ ▓▓▓▓  ▓ ▓ ▓▓▓    ▓▓▓ ▓▓  ▓  ▓▓┃    ┃▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓▓▓     ▓▓┃
┃▓▓▓ ▓▓▓   ▓  ▓▓▓ ▓▓ ▓ ▓▓▓ ▓▓▓   ┃    ┃▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓▓▓       ┃
┃▓▓ ▓▓▓▓  ▓ ▓▓▓▓   ▓▓▓▓▓▓▓   ▓   ┃    ┃▓▓▓▓▓▓▓   ▓▓▓▓▓▓  ▓▓▓▓▓▓▓       ┃
┃▓       ▓ ▓▓  ▓▓▓ ▓ ▓▓▓ ▓▓  ▓  ▓┃    ┃         ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓ ▓   ▓▓▓▓▓▓   ▓▓▓▓      ▓   ▓▓▓┃    ┃       ▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓   ▓▓ ┃
┃▓    ▓ ▓ ▓        ▓▓  ▓▓▓▓ ▓ ▓  ┃    ┃      ▓▓▓        ▓▓▓   ▓▓▓   ▓▓ ┃
┃ ▓ ▓  ▓▓         ▓ ▓   ▓▓  ▓ ▓▓ ┃    ┃      ▓▓         ▓▓▓   ▓▓    ▓▓ ┃
┃▓  ▓  ▓▓   ▓▓▓ ▓▓▓▓ ▓▓    ▓   ▓ ┃    ┃      ▓▓   ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓ ┃
┃▓▓  ▓▓ ▓ ▓▓▓ ▓▓ ▓▓▓ ▓▓    ▓▓▓▓▓ ┃    ┃    ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓ ┃
┃▓   ▓▓▓  ▓ ▓▓▓▓▓   ▓▓ ▓ ▓ ▓  ▓▓▓┃    ┃▓▓  ▓▓▓  ▓▓▓▓▓▓    ▓▓▓    ▓▓▓▓▓▓┃
┃▓▓▓▓ ▓▓ ▓▓ ▓▓      ▓ ▓  ▓ ▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓     ▓▓▓▓▓┃
┃ ▓ ▓ ▓▓▓▓   ▓▓▓  ▓ ▓▓    ▓▓▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓              ▓▓▓▓┃
┃▓  ▓▓▓▓ ▓▓ ▓ ▓  ▓▓   ▓▓▓    ▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓        ┃
┃▓▓▓▓▓▓▓ ▓▓▓  ▓ ▓  ▓   ▓▓  ▓  ▓  ┃    ┃  ▓▓▓▓▓▓▓▓            ▓▓        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓  ▓▓▓ ▓  ▓ ▓ ▓   ▓  ▓▓   ▓  ▓ ┃    ┃     ▓▓▓              ▓▓        ┃
┃▓ ▓▓ ▓▓▓▓  ▓ ▓ ▓ ▓ ▓▓▓▓▓▓▓ ▓  ▓▓┃    ┃   ▓▓▓▓▓             ▓▓▓▓▓▓   ▓▓┃
┃ ▓ ▓ ▓  ▓  ▓ ▓▓   ▓   ▓▓ ▓▓  ▓▓▓┃    ┃  ▓▓▓▓▓▓▓            ▓▓▓▓▓▓   ▓▓┃
┃   ▓▓▓▓▓  ▓    ▓▓▓   ▓▓▓▓ ▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓            ▓▓▓▓▓▓     ┃
┃▓ ▓▓▓▓ ▓▓▓   ▓     ▓▓ ▓   ▓     ┃    ┃ ▓▓▓▓▓▓▓▓           ▓▓▓         ┃
┃▓▓▓▓   ▓  ▓ ▓ ▓ ▓ ▓ ▓▓▓       ▓▓┃    ┃ ▓▓▓               ▓▓▓▓         ┃
┃     ▓    ▓▓    ▓▓ ▓   ▓▓    ▓ ▓┃    ┃                ▓▓▓▓            ┃
┃▓▓▓▓▓ ▓   ▓   ▓▓▓▓▓   ▓ ▓ ▓ ▓  ▓┃    ┃▓▓▓             ▓▓▓▓            ┃
┃▓▓▓   ▓ ▓▓▓ ▓  ▓ ▓▓▓▓▓   ▓  ▓▓ ▓┃    ┃▓▓▓     ▓▓▓▓    ▓▓▓▓▓▓▓         ┃
┃▓▓     ▓▓ ▓▓▓▓  ▓▓▓▓▓▓▓▓  ▓  ▓ ▓┃    ┃▓▓     ▓▓▓▓▓▓   ▓▓▓▓▓▓▓         ┃
┃▓▓   ▓  ▓▓▓▓  ▓▓ ▓▓  ▓ ▓       ▓┃    ┃▓▓     ▓▓▓▓▓▓   ▓▓▓▓▓▓          ┃
┃ ▓  ▓  ▓▓ ▓ ▓   ▓ ▓ ▓ ▓ ▓ ▓  ▓ ▓┃    ┃ ▓     ▓▓▓▓▓     ▓▓▓▓           ┃
┃ ▓ ▓   ▓▓▓  ▓  ▓  ▓▓ ▓  ▓ ▓ ▓ ▓▓┃    ┃ ▓▓    ▓▓▓▓       ▓▓     ▓▓▓▓▓  ┃
┃ ▓▓   ▓ ▓ ▓ ▓ ▓▓  ▓▓▓  ▓ ▓▓▓ ▓ ▓┃    ┃ ▓▓▓   ▓▓     ▓▓  ▓▓    ▓▓▓▓▓▓▓ ┃
┃  ▓▓ ▓ ▓▓ ▓   ▓▓▓▓     ▓ ▓▓▓▓   ┃    ┃ ▓▓▓  ▓▓▓     ▓▓▓▓▓▓    ▓▓▓▓▓▓▓ ┃
┃ ▓▓▓ ▓ ▓    ▓▓▓  ▓▓ ▓▓  ▓ ▓▓▓▓▓▓┃    ┃ ▓▓▓  ▓▓         ▓▓▓    ▓▓▓▓▓▓▓ ┃
┃ ▓▓   ▓▓ ▓▓ ▓ ▓  ▓▓▓ ▓  ▓▓ ▓ ▓▓ ┃    ┃ ▓▓▓  ▓▓ ▓▓      ▓▓▓    ▓▓▓▓▓▓▓ ┃
┃▓  ▓▓ ▓▓ ▓▓  ▓  ▓▓▓    ▓▓  ▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓ ▓▓      ▓▓▓    ▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓▓▓▓ ▓     ▓▓  ▓ ▓  ▓▓ ▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓          ░░    ▓▓▓▓▓▓▓▓┃
┃   ▓   ▓   ▓      ▓ ▓ ▓ ▓▓▓  ▓ ▓┃    ┃   ░░  ▓          ░░    ▓▓  ▓▓▓▓┃
┃▓ ▓▓▓  ▓   ▓▓▓▓▓  ▓▓    ▓▓  ▓▓▓▓┃    ┃   ░░  ▓      ▓▓  ▓▓    ▓▓   ▓▓▓┃
┃   ▓ ▓▓▓ ▓    ▓▓ ▓ ▓   ▓ ▓   ▓ ▓┃    ┃   ░░ ▓▓      ▓▓▓▓▓▓    ▓▓   ▓▓▓┃
┃   ▓  ▓▓      ▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓ ┃    ┃   ▓▓ ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓  ▓▓ ▓ ▓▓   ▓ ▓  ▓▓▓▓▓▓  ▓    ▓┃    ┃   ▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓   ▓▓    ▓▓ ▓ ▓ ▓ ▓ ▓▓▓▓▓  ▓   ┃    ┃   ▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃▓ ▓▓       ▓▓ ▓   ▓  ▓ ▓   ▓ ▓  ┃    ┃▓▓▓▓▓      ▓▓▓▓▓▓▓▓   ▓▓▓       ┃
┃▓▓▓ ▓ ▓▓▓▓ ▓▓▓ ▓▓▓     ▓▓▓▓     ┃    ┃▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓     ┃
┃   ▓ ▓ ▓  ▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓ ▓▓ ▓  ┃    ┃      ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃   ▓▓  ▓▓▓  ▓    ▓▓ ▓▓  ▓▓▓ ▓  ▓┃    ┃       ▓▓▓  ▓▓   ▓▓▓▓▓▓▓▓▓▓░    ┃
┃▓▓    ▓  ▓  ▓▓  ▓ ▓   ▓▓▓    ▓▓ ┃    ┃       ▓▓▓        ▓▓▓▓▓▓▓   ▓▓▓ ┃
┃ ▓▓   ▓▓ ▓▓     ▓▓  ▓▓  ▓   ▓▓▓ ┃    ┃ ▓▓   ▓▓▓▓          ▓▓      ▓▓▓ ┃
┃ ▓▓ ▓ ▓▓▓▓     ▓▓ ▓ ▓▓  ▓▓ ▓▓ ▓▓┃    ┃ ▓▓   ▓▓▓▓          ▓▓      ▓▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

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┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓   ▓▓▓   ▓▓▓ ▓ ▓ ▓▓ ▓▓▓  ▓ ▓ ┃    ┃      ▓▓    ▓▓▓▓▓▓▓▓▓░░░▓▓      ┃
┃▓  ▓▓▓▓  ▓ ▓▓▓▓▓▓▓ ▓▓ ▓ ▓▓ ▓  ▓▓┃    ┃      ▓▓▓░░▓▓▓▓▓▓▓▓▓▓░░░▓▓      ┃
┃ ▓     ▓▓ ▓▓▓▓▓▓▓▓ ▓▓  ▓▓  ▓▓▓  ┃    ┃      ▓▓▓░░▓▓▓▓▓▓▓▓▓▓       ▓▓  ┃
┃  ▓  ▓▓▓▓▓  ▓▓       ▓▓     ▓▓  ┃    ┃      ▓▓▓   ▓▓▓             ▓▓  ┃
┃ ▓  ▓  ▓     ▓▓▓ ▓ ▓  ▓     ▓▓  ┃    ┃     ▓▓▓▓   ▓▓▓             ▓▓  ┃
┃ ▓▓▓ ▓▓▓▓ ▓ ▓    ▓       ▓▓▓  ▓▓┃    ┃     ▓▓▓▓▓▓░░             ▓▓▓▓▓▓┃
┃     ▓▓ ▓▓▓▓ ▓ ▓▓ ▓▓▓    ▓ ▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓░░    ▓▓▓▓     ▓▓▓▓▓▓┃
┃▓ ▓   ▓▓ ▓▓    ▓  ▓▓▓▓▓▓  ▓▓ ▓  ┃    ┃     ▓▓▓▓▓▓░░  ▓▓▓▓▓▓▓    ▓▓▓   ┃
┃ ▓▓▓ ▓    ▓▓ ▓▓▓▓   ▓▓  ▓ ▓▓  ▓ ┃    ┃   ▓▓▓     ░▓▓▓▓▓   ▓▓    ▓▓▓   ┃
┃   ▓▓▓  ▓   ▓▓  ▓▓  ▓  ▓   ▓▓  ▓┃    ┃   ▓▓▓     ▓▓▓▓▓▓          ▓▓   ┃
┃      ▓▓   ▓ ▓ ▓ ▓  ▓ ▓▓▓   ▓▓ ▓┃    ┃     ▓     ▓▓▓▓▓      ▓▓        ┃
┃▓▓▓▓▓ ▓ ▓▓▓  ▓ ▓   ▓  ▓▓    ▓ ▓ ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓        ┃
┃▓    ▓ ▓▓ ▓▓▓▓▓▓  ▓▓▓▓ ▓ ▓▓   ▓ ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓     ┃
┃▓▓   ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓  ▓▓▓  ▓  ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓     ┃
┃▓▓  ▓  ▓▓ ▓▓▓▓  ▓   ▓  ▓▓   ▓▓ ▓┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓          ┃
┃  ▓ ▓▓▓ ▓▓▓▓ ▓▓▓ ▓▓▓▓▓▓       ▓ ┃    ┃▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓          ┃
┃▓▓▓ ▓     ▓ ▓  ▓ ▓▓▓▓▓   ▓ ▓▓▓ ▓┃    ┃▓▓              ▓▓▓▓▓▓    ▓▓▓▓  ┃
┃▓  ▓  ▓▓    ▓  ▓   ▓   ▓ ▓▓▓ ▓ ▓┃    ┃                   ▓▓▓    ▓▓▓▓  ┃
┃▓   ▓▓▓ ▓▓▓▓ ▓  ▓▓ ▓▓ ▓▓ ▓ ▓▓▓  ┃    ┃    ▓▓▓▓▓▓▓▓    ▓▓        ▓▓▓▓  ┃
┃▓   ▓▓▓▓▓ ▓▓ ▓  ▓▓ ▓ ▓ ▓  ▓ ▓▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓    ▓▓        ▓▓▓▓  ┃
┃▓ ▓ ▓▓▓▓▓▓ ▓  ▓▓▓▓      ▓ ▓▓▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓▓▓  ┃
┃     ▓▓▓▓▓ ▓ ▓▓ ▓▓ ▓▓ ▓ ▓ ▓▓▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃▓▓▓  ▓   ▓▓ ▓ ▓  ▓  ▓▓ ▓▓▓▓▓▓▓▓ ┃    ┃         ▓▓▓▓         ░▓▓▓▓▓▓▓▓▓┃
┃  ▓  ▓   ▓▓▓   ▓      ▓▓▓▓▓ ▓▓ ▓┃    ┃         ▓▓▓▓        ░░▓▓▓▓▓▓▓▓ ┃
┃  ▓    ▓   ▓▓▓ ▓  ▓ ▓▓ ▓  ▓▓    ┃    ┃           ▓▓        ░░▓▓▓▓▓    ┃
┃▓ ▓    ▓    ▓ ▓      ▓  ▓▓▓   ▓▓┃    ┃           ░░       ▓▓  ▓▓▓▓  ▓▓┃
┃▓        ▓ ▓  ▓▓▓▓ ▓▓▓▓  ▓▓▓▓ ▓▓┃    ┃            ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓  ▓▓┃
┃ ▓  ▓  ▓ ▓▓ ▓▓ ▓▓▓ ▓    ▓▓▓    ▓┃    ┃            ▓▓▓▓▓▓▓▓▓▓   ▓▓   ▓▓┃
┃▓▓▓▓▓▓ ▓▓    ▓ ▓▓▓▓ ▓▓ ▓  ▓   ▓▓┃    ┃            ▓▓▓▓▓▓▓▓▓▓▓         ┃
┃  ▓   ▓  ▓  ▓ ▓▓  ▓  ▓▓▓▓  ▓▓▓ ▓┃    ┃            ▓▓▓▓▓    ▓▓   ▓▓▓   ┃
┃     ▓ ▓    ▓▓▓ ▓   ▓     ▓▓    ┃    ┃            ▓▓▓▓▓         ▓▓▓   ┃
┃▓   ▓▓▓    ▓▓  ▓ ▓▓▓▓▓  ▓ ▓▓▓▓  ┃    ┃                          ▓▓▓   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

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┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓▓▓  ▓    ▓▓   ▓▓▓ ▓▓▓▓▓▓▓ ┃    ┃     ▓▓▓       ▓▓   ▓▓▓▓▓▓▓▓▓▓  ┃
┃   ▓   ▓▓▓▓ ▓▓▓▓▓   ▓▓▓▓▓ ▓▓▓▓ ▓┃    ┃    ▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓▓▓▓ ▓▓▓   ▓ ▓▓▓    ▓▓▓▓ ▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓ ▓▓▓▓ ▓   ▓▓▓  ▓▓▓▓ ▓ ▓  ▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓ ▓▓ ▓▓▓ ▓▓  ▓ ▓▓▓▓▓▓ ▓▓▓▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃  ▓ ▓   ▓▓▓ ▓▓ ▓▓  ▓  ▓  ▓ ▓ ▓ ▓┃    ┃ ▓▓▓▓   ▓▓░░▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓   ┃
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┃  ▓  ▓▓▓▓▓ ▓▓  ▓    ▓▓▓      ▓▓ ┃    ┃  ▓  ▓▓▓▓▓▓▓▓  ▓           ▓▓   ┃
┃▓ ▓▓▓  ▓▓  ▓▓  ▓▓▓▓ ▓    ▓▓▓▓ ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓             ┃
┃   ▓▓▓   ▓ ▓▓▓▓  ▓▓   ▓ ▓  ▓ ▓▓ ┃    ┃  ▓▓▓▓   ▓▓▓▓  ▓▓▓▓             ┃
┃  ▓▓ ▓ ▓ ▓▓ ▓  ▓▓▓▓▓ ▓ ▓   ▓    ┃    ┃  ▓▓▓    ▓▓▓   ▓▓▓▓░░           ┃
┃▓▓▓    ▓  ▓   ▓▓▓▓▓ ▓ ▓ ▓▓   ▓  ┃    ┃         ▓▓    ▓▓▓▓░░░          ┃
┃        ▓▓▓ ▓  ▓▓▓     ▓▓ ▓▓ ▓ ▓┃    ┃         ▓▓    ▓▓▓▓  ░░   ▓▓    ┃
┃  ▓▓ ▓▓▓  ▓ ▓ ▓▓  ▓  ▓▓   ▓▓ ▓▓ ┃    ┃          ▓    ▓▓▓   ▓▓   ▓▓    ┃
┃▓▓    ▓   ▓     ▓▓  ▓▓▓  ▓ ▓    ┃    ┃      ▓▓  ▓    ▓▓▓  ▓▓▓   ▓▓    ┃
┃  ▓   ▓▓▓▓▓▓  ▓ ▓▓ ▓▓ ▓▓▓▓ ▓ ▓ ▓┃    ┃      ▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓▓       ┃
┃▓ ▓ ▓   ▓▓ ▓ ▓ ▓ ▓  ▓▓ ▓    ▓▓▓ ┃    ┃        ▓▓▓▓▓   ▓▓    ▓▓▓▓      ┃
┃▓▓ ▓▓▓▓ ▓  ▓▓   ▓▓▓   ▓ ▓▓▓  ▓ ▓┃    ┃    ▓▓  ▓  ▓▓   ▓▓     ▓▓▓▓     ┃
┃  ▓  ▓  ▓  ▓▓▓  ▓    ▓  ▓ ▓▓ ▓  ┃    ┃   ░▓▓  ▓  ▓▓▓          ▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓▓  ▓  ▓  ▓▓ ▓▓ ▓    ▓▓ ▓▓ ▓┃    ┃        ▓  ▓▓▓▓▓        ▓▓▓▓▓▓▓ ┃
┃       ▓▓ ▓▓ ▓▓▓   ▓    ▓▓▓▓▓ ▓ ┃    ┃        ▓▓▓▓  ▓▓        ▓▓▓▓▓▓▓ ┃
┃  ▓▓▓  ▓ ▓▓      ▓▓▓ ▓▓▓▓ ▓  ▓▓ ┃    ┃                  ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓ ▓ ▓▓           ▓▓▓ ▓ ▓  ▓ ▓  ┃    ┃                 ▓▓▓▓▓▓▓   ▓▓▓▓ ┃
┃  ▓     ▓▓▓▓▓  ▓ ▓▓ ▓▓▓▓   ▓▓▓▓ ┃    ┃          ▓▓     ▓▓▓▓▓▓▓   ▓▓▓  ┃
┃▓ ▓▓▓ ▓▓  ▓   ▓  ▓▓▓▓ ▓  ▓▓▓▓▓  ┃    ┃  ▓▓▓     ▓▓     ▓▓▓▓▓▓▓  ▓▓▓▓  ┃
┃   ▓▓     ▓▓ ▓  ▓ ▓ ▓ ▓▓▓ ▓  ▓ ▓┃    ┃  ▓▓▓     ▓      ▓▓▓  ▓▓▓▓▓▓▓   ┃
┃  ▓▓   ▓▓▓   ▓▓   ▓     ▓ ▓▓▓   ┃    ┃       ▓▓▓▓      ▓▓▓  ░▓▓▓▓▓▓   ┃
┃     ▓ ▓▓▓▓ ▓▓  ▓▓▓▓▓▓ ▓  ▓▓▓ ▓▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░▓▓▓▓▓▓▓ ┃
┃▓ ▓▓ ▓▓ ▓ ▓▓▓ ▓▓▓▓  ▓ ▓ ▓ ▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░░▓▓▓▓▓▓ ┃
┃▓▓▓▓▓ ▓▓ ▓ ▓  ▓▓▓  ▓   ▓ ▓   ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓               ┃
┃  ▓ ▓    ▓  ▓▓▓ ▓   ▓ ▓▓▓      ▓┃    ┃              ▓▓                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓     ▓▓▓  ▓▓▓ ▓▓▓▓▓▓▓▓▓  ▓ ▓▓┃    ┃              ▓▓▓▓▓▓▓▓          ┃
┃  ▓ ▓▓▓▓   ▓▓ ▓▓ ▓▓▓    ▓ ▓▓ ▓▓ ┃    ┃    ░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░▓▓░   ┃
┃  ▓ ▓  ▓▓▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓ ▓▓▓▓ ▓▓┃    ┃     ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░▓▓    ┃
┃ ▓▓▓ ▓ ▓ ▓▓▓  ▓▓  ▓ ▓ ▓      ▓  ┃    ┃      ▓▓▓▓▓▓▓▓▓▓    ░░          ┃
┃▓ ▓  ▓ ▓▓▓   ▓▓▓  ▓  ▓   ▓▓▓ ▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓▓▓    ░░          ┃
┃▓    ▓▓  ▓▓▓ ▓▓▓▓▓ ▓▓  ▓  ▓ ▓▓  ┃    ┃      ▓▓▓▓▓▓▓▓▓▓    ▓▓    ▓▓▓▓  ┃
┃ ▓     ▓▓▓▓ ▓▓      ▓▓▓ ▓ ▓▓ ▓▓▓┃    ┃       ▓▓▓▓▓▓▓     ▓▓▓▓   ▓▓▓▓▓ ┃
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┃     ▓▓▓▓▓▓▓ ▓ ▓  ▓▓▓▓▓▓ ▓▓  ▓▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓  ▓▓▓┃
┃  ▓▓▓▓ ▓  ▓ ▓▓ ▓▓ ▓▓  ▓   ▓  ▓▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓  ▓▓▓┃
┃▓  ▓▓   ▓ ▓ ▓      ▓▓ ▓▓▓▓▓▓  ▓▓┃    ┃   ▓▓▓  ▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓   ▓▓  ▓▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓┃    ┃        ▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃        ▓ ▓▓ ▓▓  ▓ ▓▓▓ ▓▓▓ ▓ ▓▓▓┃    ┃        ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓  ▓▓▓▓┃
┃ ▓▓▓  ▓ ▓  ▓▓▓ ▓ ▓     ▓▓     ▓▓┃    ┃ ▓▓       ▓▓▓▓         ▓▓     ▓▓┃
┃▓▓▓ ▓▓    ▓▓ ▓   ▓ ▓ ▓  ▓       ┃    ┃▓▓▓▓▓▓     ▓▓                   ┃
┃▓▓▓▓▓▓  ▓   ▓    ▓         ▓ ▓ ▓┃    ┃▓▓▓▓▓▓                          ┃
┃▓▓  ▓▓ ▓  ▓ ▓  ▓    ▓   ▓ ▓▓▓▓▓▓┃    ┃▓▓  ▓▓▓    ▓▓             ▓▓▓▓▓▓┃
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┃▓▓▓▓▓  ▓▓▓▓▓▓     ▓     ▓ ▓     ┃    ┃▓▓▓▓▓  ░░               ░░      ┃
┃▓▓▓ ▓▓▓       ▓▓▓▓▓ ▓▓▓▓      ▓▓┃    ┃▓▓▓▓▓▓▓▓░      ▓▓▓▓ ▓▓▓░░       ┃
┃▓    ▓▓▓▓ ▓   ▓  ▓▓ ▓▓▓ ▓ ▓   ▓ ┃    ┃▓▓  ▓▓▓▓░     ▓▓▓▓▓ ▓▓▓░        ┃
┃▓▓  ▓ ▓ ▓   ▓▓ ▓▓▓    ▓▓ ▓ ▓ ▓  ┃    ┃    ░░░░░     ▓▓▓▓   ▓▓         ┃
┃▓  ▓▓    ▓ ▓ ▓ ▓▓▓   ▓▓  ▓  ▓ ▓ ┃    ┃    ░░░░░░░░░░▓▓▓▓   ▓▓         ┃
┃  ▓ ▓▓▓▓▓ ▓▓▓ ▓▓▓▓ ▓▓▓ ▓   ▓▓ ▓ ┃    ┃   ▓▓▓▓▓░░▓▓░░▓▓▓▓▓▓▓▓▓    ▓▓▓  ┃
┃▓▓▓ ▓  ▓  ▓▓   ▓  ▓▓▓▓▓▓ ▓ ▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓▓▓    ▓▓▓░ ┃
┃▓ ▓▓ ▓ ▓ ▓ ▓  ▓▓▓▓ ▓ ▓       ▓ ▓┃    ┃ ▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓          ┃
┃ ▓▓ ▓▓ ▓    ▓▓▓ ▓ ▓▓▓▓     ▓  ▓▓┃    ┃       ▓     ▓▓▓▓▓▓▓▓▓          ┃
┃   ▓   ▓ ▓    ▓▓▓ ▓ ▓▓▓ ▓▓▓▓▓  ▓┃    ┃       ▓▓    ▓▓▓▓▓▓▓▓▓▓   ▓▓    ┃
┃▓ ▓▓   ▓▓ ▓  ▓▓▓ ▓▓ ▓ ▓  ▓ ▓   ▓┃    ┃       ▓▓     ▓▓▓▓▓▓▓▓▓   ▓▓    ┃
┃▓   ▓ ▓▓▓ ▓▓    ▓  ▓▓▓▓ ▓  ▓    ┃    ┃       ▓▓           ▓▓▓         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓  ▓▓ ▓▓ ▓▓ ▓  ▓ ┃    ┃    ▓▓▓▓▓▓        ▓▓    ▓▓      ┃
┃   ▓  ▓▓▓▓    ▓▓  ▓▓  ▓ ▓▓ ▓    ┃    ┃    ▓▓▓▓▓▓        ▓▓    ▓▓▓▓    ┃
┃   ▓ ▓▓  ▓  ▓  ▓ ▓▓▓      ▓▓▓▓▓▓┃    ┃      ▓▓         ▓▓▓     ▓▓▓▓▓▓▓┃
┃▓▓    ▓▓  ▓▓▓  ▓▓ ▓   ▓▓ ▓ ▓▓ ▓▓┃    ┃                 ▓▓      ▓▓▓▓▓▓▓┃
┃▓ ▓▓▓   ▓▓       ▓▓    ▓ ▓▓▓ ▓  ┃    ┃▓▓▓▓    ▓▓       ▓▓      ▓▓▓▓   ┃
┃▓ ▓▓ ▓  ▓▓   ▓ ▓ ▓ ▓▓ ▓  ▓▓     ┃    ┃▓▓▓▓    ▓▓               ▓▓     ┃
┃▓    ▓ ▓▓ ▓▓ ▓ ▓    ▓ ▓ ▓▓    ▓▓┃    ┃   ▓▓▓▓▓▓▓▓            ▓▓▓    ▓▓┃
┃▓  ▓▓▓▓ ▓▓▓  ▓▓  ▓▓ ▓  ▓▓▓    ▓▓┃    ┃   ▓▓▓▓▓▓▓▓           ░▓▓▓    ▓▓┃
┃ ▓ ▓▓   ▓  ▓   ▓▓   ▓ ▓▓▓▓▓    ▓┃    ┃ ▓▓▓▓▓▓▓▓            ░░▓▓▓▓   ▓▓┃
┃▓▓▓▓  ▓▓▓  ▓▓ ▓ ▓    ▓   ▓▓▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓           ░░  ▓▓▓▓▓▓▓▓┃
┃▓▓▓  ▓▓  ▓ ▓  ▓▓   ▓▓  ▓▓  ▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓           ░░  ▓▓▓▓▓▓▓▓┃
┃▓▓ ▓▓▓▓▓ ▓  ▓      ▓ ▓▓ ▓ ▓▓ ▓ ▓┃    ┃▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓▓    ┃
┃  ▓     ▓   ▓    ▓▓▓▓ ▓▓▓▓▓     ┃    ┃ ▓▓▓▓▓             ▓▓▓▓▓▓▓▓     ┃
┃ ▓▓ ▓▓ ▓  ▓  ▓      ▓ ▓ ▓▓  ▓▓▓ ┃    ┃ ▓▓▓▓▓              ▓▓▓▓▓▓▓  ▓▓ ┃
┃▓ ▓▓▓▓ ▓    ▓   ▓    ▓▓▓▓▓▓▓  ▓▓┃    ┃ ▓▓▓▓▓              ▓▓▓▓▓▓▓  ▓▓ ┃
┃▓▓▓▓▓  ▓ ▓▓▓    ▓▓▓ ▓ ▓▓▓▓▓ ▓▓ ▓┃    ┃ ▓▓▓▓           ▓▓▓▓▓▓▓▓▓▓▓     ┃
┃▓ ▓▓   ▓   ▓   ▓▓ ▓▓▓▓ ▓ ▓    ▓ ┃    ┃ ▓▓▓▓          ▓▓▓▓▓▓▓▓▓▓       ┃
┃  ▓▓▓▓▓   ▓  ▓▓▓▓▓ ▓▓▓ ▓▓   ▓   ┃    ┃  ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃▓ ▓ ▓▓    ▓▓▓▓▓ ▓▓▓     ▓ ▓ ▓▓▓▓┃    ┃   ▓▓▓    ▓▓▓▓▓▓▓▓▓▓        ▓▓▓▓┃
┃▓  ▓▓   ▓▓▓▓▓▓▓  ▓ ▓      ▓ ▓ ▓▓┃    ┃    ▓▓   ▓▓▓▓▓▓  ▓▓▓      ▓▓▓▓▓▓┃
┃▓   ▓▓ ▓  ▓▓▓ ▓  ▓▓  ▓ ▓▓ ▓▓▓ ▓ ┃    ┃    ▓▓   ▓▓▓▓▓▓  ▓▓▓      ▓▓▓▓▓ ┃
┃    ▓    ▓  ▓▓ ▓ ▓ ▓▓   ▓ ▓▓ ▓ ▓┃    ┃    ▓▓   ▓▓▓▓▓   ▓▓▓      ▓▓▓▓  ┃
┃ ▓▓▓▓▓▓  ▓▓ ▓▓▓  ▓▓▓    ▓  ▓ ▓  ┃    ┃  ▓▓▓▓   ▓▓▓▓▓   ▓▓▓      ▓▓▓▓  ┃
┃ ▓ ▓ ▓ ▓▓▓▓  ▓    ▓ ▓ ▓ ▓ ▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓              ▓▓▓    ┃
┃   ▓ ▓▓ ▓▓▓  ▓   ▓     ▓ ▓▓▓    ┃    ┃   ▓▓▓▓▓▓▓▓             ▓▓▓▓    ┃
┃   ▓ ▓▓ ▓▓▓▓ ▓▓         ▓▓▓▓ ▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓            ▓▓▓▓    ┃
┃    ▓▓ ▓▓▓▓▓   ▓▓▓▓ ▓▓▓ ▓   ▓  ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓      ┃
┃   ▓▓▓    ▓▓▓ ▓▓   ▓    ▓▓   ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓      ┃
┃  ▓ ▓  ▓▓▓ ▓▓▓▓▓▓  ▓▓▓▓ ▓▓ ▓   ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓ ▓▓      ┃
┃▓ ▓▓▓▓ ▓ ▓▓▓▓▓  ▓ ▓  ▓▓      ▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓         ┃
┃ ▓    ▓▓▓  ▓▓▓▓ ▓▓▓    ▓ ▓▓▓ ▓▓ ┃    ┃      ▓▓  ▓▓▓▓▓▓▓▓▓             ┃
┃▓ ▓ ▓ ▓▓  ▓   ▓  ▓▓  ▓▓  ▓  ▓▓ ▓┃    ┃      ▓▓         ▓▓             ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓    ▓▓▓ ▓  ▓ ▓▓▓▓  ▓▓ ▓▓  ▓ ▓┃    ┃        ▓▓        ▓▓            ┃
┃ ▓  ▓  ▓ ▓ ▓▓▓ ▓  ▓▓    ▓ ▓ ▓▓▓▓┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓  ┃
┃   ▓▓▓   ▓▓▓ ▓ ▓▓      ▓ ▓▓ ▓   ┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓  ┃
┃▓    ▓▓▓ ▓▓▓▓ ▓ ▓▓▓▓▓▓  ▓▓ ▓▓ ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓  ┃
┃ ▓▓  ▓▓ ▓▓▓   ▓▓▓  ▓▓▓▓    ▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓ ┃
┃  ▓▓  ▓  ▓▓▓▓ ▓ ▓ ▓▓ ▓▓▓▓▓  ▓▓▓▓┃    ┃         ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓  ▓▓▓ ┃
┃▓▓         ▓ ▓ ▓▓   ▓▓   ▓▓ ▓   ┃    ┃         ▓▓▓▓░▓▓▓       ▓▓▓▓▓▓▓ ┃
┃ ▓  ▓  ▓▓▓▓ ▓  ▓  ▓     ▓▓▓ ▓▓▓▓┃    ┃        ▓▓▓▓░░░▓▓        ▓▓▓▓▓▓▓┃
┃▓ ▓▓     ▓   ▓▓▓▓ ▓▓ ▓▓▓  ▓▓▓  ▓┃    ┃ ▓▓▓    ▓▓▓░░░░▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓┃
┃▓ ▓▓ ▓  ▓▓▓ ▓   ▓ ▓ ▓▓▓  ▓▓   ▓▓┃    ┃ ▓▓▓      ░░░░  ▓▓▓▓▓▓▓   ▓▓▓▓▓▓┃
┃ ▓▓▓  ▓▓   ▓ ▓▓ ▓▓▓▓ ▓ ▓▓  ▓▓▓▓▓┃    ┃ ▓▓▓▓     ▓▓▓▓  ▓▓▓▓▓▓▓     ▓▓▓▓┃
┃▓ ▓ ▓▓   ▓▓▓ ▓  ▓  ▓▓▓▓ ▓    ▓ ▓┃    ┃ ▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓┃
┃▓▓▓▓▓ ▓▓  ▓ ▓▓▓ ▓▓  ▓▓ ▓▓ ▓▓▓▓▓ ┃    ┃ ▓▓▓▓      ▓▓▓▓▓▓░  ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃   ▓▓▓   ▓   ▓▓ ▓    ▓▓ ▓▓▓ ▓ ▓▓┃    ┃  ▓▓▓       ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓    ▓▓▓ ▓▓▓ ▓ ▓ ▓  ▓▓     ▓  ┃    ┃  ▓▓▓  ▓▓   ▓▓▓▓▓▓    ▓▓▓▓▓▓▓   ┃
┃ ▓▓▓ ▓▓▓▓  ▓ ▓▓▓▓▓ ▓▓  ▓▓▓ ▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓    ▓▓▓▓▓▓   ┃
┃▓▓  ▓ ▓▓▓   ▓ ▓ ▓ ▓     ▓ ▓▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓    ▓▓▓▓▓▓ ▓▓┃
┃▓▓▓ ▓▓▓▓▓▓▓  ▓▓ ▓▓ ▓ ▓▓▓▓▓    ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓░░░░▓▓▓    ▓▓┃
┃ ▓ ▓▓▓▓▓ ▓▓  ▓▓▓▓▓▓ ▓ ▓  ▓    ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓░░░░▓▓▓      ┃
┃▓▓ ▓▓ ▓ ▓▓▓▓ ▓▓ ▓  ▓▓▓  ▓▓▓▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓    ┃
┃ ▓ ▓▓ ▓ ▓▓▓▓▓ ▓▓  ▓ ▓ ▓ ▓ ▓▓▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓▓▓▓▓ ▓ ▓▓▓   ▓  ▓▓▓ ▓    ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓       ┃
┃ ▓▓  ▓  ▓ ▓▓ ▓▓▓  ▓▓ ▓▓ ▓  ▓ ▓▓▓┃    ┃ ▓▓    ▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓   ▓▓▓▓┃
┃▓▓   ▓ ▓▓  ▓▓ ▓   ▓▓▓ ▓ ▓▓  ▓  ▓┃    ┃ ▓▓    ▓▓  ▓▓▓    ▓▓▓▓▓▓▓   ▓▓▓▓┃
┃  ▓ ▓  ▓    ▓ ▓ ▓ ▓ ▓▓▓▓▓   ▓▓▓▓┃    ┃       ▓   ▓▓▓    ▓▓▓▓▓▓▓   ▓▓▓▓┃
┃ ▓▓   ▓▓  ▓ ▓▓    ▓  ▓▓▓▓ ▓▓▓▓ ▓┃    ┃      ▓▓   ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃   ▓ ▓▓▓▓▓▓▓▓  ▓▓▓ ▓ ▓ ▓▓▓▓  ▓▓▓┃    ┃      ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓  ▓ ▓▓▓ ▓ ▓▓ ▓▓ ▓▓  ▓ ▓▓▓▓ ▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓ ▓        ▓ ▓▓ ▓ ▓ ▓ ▓▓▓ ▓▓  ┃    ┃▓▓▓   ▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓   ▓▓ ▓ ▓ ▓  ▓▓▓▓  ▓ ▓  ▓ ▓   ┃    ┃▓▓▓   ▓▓       ▓▓▓▓▓▓░▓▓▓▓      ┃
┃ ▓▓▓  ▓▓▓ ▓▓▓   ▓ ▓▓▓ ▓▓▓▓    ▓ ┃    ┃ ▓▓   ▓▓       ▓▓▓▓▓░░░▓▓       ┃
┃  ▓ ▓   ▓  ▓   ▓▓ ▓▓  ▓ ▓      ▓┃    ┃                 ▓▓▓            ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓▓▓ ▓ ▓     ▓▓▓▓▓    ▓    ▓▓▓┃    ┃   ▓▓▓          ▓▓▓          ▓▓ ┃
┃▓  ▓▓▓ ▓     ▓  ▓▓  ▓▓ ▓ ▓▓▓▓▓▓ ┃    ┃   ▓▓▓          ▓▓▓▓▓     ▓▓▓▓▓ ┃
┃ ▓   ▓  ▓ ▓     ▓▓▓▓▓     ▓▓  ▓ ┃    ┃   ▓▓▓          ▓▓▓▓▓     ▓▓  ▓ ┃
┃▓▓▓▓ ▓ ▓ ▓ ▓ ▓▓    ▓▓ ▓ ▓     ▓▓┃    ┃ ▓▓▓▓▓             ▓▓▓        ▓ ┃
┃  ▓▓▓    ▓▓   ▓▓▓   ▓▓  ▓▓  ▓▓  ┃    ┃ ▓▓▓▓▓        ▓▓   ▓▓▓░░▓▓   ▓▓ ┃
┃▓▓  ▓▓▓▓▓▓ ▓▓ ▓▓ ▓ ▓▓▓▓ ▓▓▓  ▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓░░▓▓   ▓▓ ┃
┃ ▓▓▓▓▓▓▓   ▓ ▓ ▓ ▓ ▓   ▓▓▓  ▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓      ┃
┃▓  ▓▓  ▓▓ ▓▓▓ ▓▓ ▓▓▓▓ ▓    ▓  ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░         ┃
┃ ▓ ▓▓ ▓▓▓▓▓  ▓▓▓▓▓▓▓ ▓  ▓▓▓ ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓     ▓▓▓ ▓▓ ▓▓▓  ▓ ▓ ▓▓   ▓  ▓ ┃    ┃ ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓▓▓▓▓  ▓ ▓▓ ▓▓▓ ▓ ▓▓▓▓▓   ▓▓▓▓ ▓┃    ┃ ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓ ┃
┃ ▓▓  ▓     ▓  ▓  ▓▓▓  ▓  ▓▓▓ ▓ ▓┃    ┃ ▓▓▓▓    ▓▓▓     ▓▓▓▓▓   ▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓  ▓ ▓▓  ▓ ▓ ▓▓▓▓   ▓▓▓  ▓▓┃    ┃ ▓▓▓▓    ▓▓▓      ▓▓▓    ▓▓▓▓▓▓▓┃
┃▓ ▓▓  ▓▓ ▓▓▓▓   ▓▓ ▓▓   ▓ ▓▓ ▓▓▓┃    ┃ ▓▓▓▓  ▓▓▓▓▓      ▓▓▓    ▓▓▓▓▓▓▓┃
┃▓ ▓▓▓  ▓▓▓▓▓ ▓ ▓      ▓▓▓  ▓▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓          ▓▓▓  ▓▓▓▓ ┃
┃   ▓▓▓▓▓  ▓▓  ▓   ▓▓  ▓▓▓▓   ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓          ▓▓▓       ┃
┃▓▓ ▓▓    ▓  ▓▓▓      ▓▓▓   ▓   ▓┃    ┃  ▓▓▓▓▓               ▓▓▓       ┃
┃▓ ▓ ▓▓▓   ▓  ▓ ▓▓▓    ▓▓▓▓     ▓┃    ┃  ▓▓▓▓▓        ▓▓▓    ▓▓▓       ┃
┃  ▓   ▓    ▓  ▓▓ ▓  ▓ ▓▓▓ ▓▓▓  ▓┃    ┃  ▓            ▓▓▓    ▓▓▓▓▓▓▓   ┃
┃ ▓▓  ▓ ▓       ▓ ▓  ▓▓ ▓ ▓▓ ▓ ▓ ┃    ┃ ▓▓            ▓▓▓     ▓▓▓▓▓▓   ┃
┃▓▓▓ ▓   ▓▓ ▓   ▓▓ ▓ ▓   ▓ ▓ ▓ ▓ ┃    ┃▓▓▓     ▓▓▓    ▓▓   ▓▓   ▓▓▓▓▓▓ ┃
┃▓▓▓     ▓▓▓▓ ▓▓▓  ▓ ▓▓▓   ▓ ▓▓▓▓┃    ┃▓▓▓     ▓▓▓▓▓▓▓▓    ▓▓   ▓▓▓▓▓▓▓┃
┃▓▓▓▓▓▓ ▓ ▓▓ ▓  ▓ ▓  ▓  ▓ ▓▓▓ ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓ ▓ ▓▓   ▓  ▓▓     ▓▓▓▓▓▓  ▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓ ▓ ▓▓  ▓▓▓▓▓▓▓▓▓▓▓ ▓ ▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃   ▓ ▓▓ ▓▓▓  ▓  ▓ ▓▓  ▓▓▓▓  ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓▓▓▓ ▓ ▓     ▓▓ ▓▓  ▓▓▓▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓     ▓   ▓  ▓    ▓▓▓ ▓▓ ▓ ▓ ▓ ┃    ┃ ▓  ▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓  ▓▓▓  ▓▓ ▓ ▓ ▓▓▓   ▓    ▓▓ ▓▓┃    ┃ ▓  ▓▓▓▓▓▓░   ▓▓▓▓▓▓▓▓   ▓▓▓▓   ┃
┃▓▓▓▓▓ ▓▓ ▓  ▓ ▓▓▓ ▓ ▓▓   ▓▓▓   ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ▓▓▓    ┃
┃ ▓ ▓ ▓▓ ▓▓▓   ▓  ▓▓▓ ▓▓  ▓▓▓  ▓ ┃    ┃ ▓▓▓▓▓▓▓░▓▓     ▓▓▓▓▓▓   ▓▓▓    ┃
┃▓  ▓▓    ▓▓ ▓▓  ▓▓▓▓ ▓   ▓  ▓ ▓ ┃    ┃         ▓▓      ▓▓▓            ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓ ▓▓  ▓▓▓▓▓▓  ▓  ▓▓▓ ▓▓   ▓▓▓ ┃    ┃    ▓▓   ▓▓        ▓▓▓▓▓▓    ▓▓ ┃
┃ ▓  ▓▓ ▓  ▓    ▓ ▓▓▓▓▓ ▓▓▓ ▓  ▓▓┃    ┃    ▓▓   ▓▓       ▓▓▓▓▓▓▓    ▓▓ ┃
┃ ▓ ▓▓▓▓  ▓▓  ▓▓▓▓ ▓▓  ▓▓▓    ▓ ▓┃    ┃    ▓▓░▓▓▓▓  ▓▓   ▓▓▓▓▓▓▓       ┃
┃▓▓▓  ▓ ▓▓▓▓ ▓▓   ▓▓▓ ▓▓▓▓  ▓    ┃    ┃     ░▓▓▓▓▓░░▓▓   ▓▓  ▓▓▓       ┃
┃▓  ▓  ▓   ▓ ▓ ▓    ▓  ▓▓ ▓   ▓ ▓┃    ┃░    ▓▓▓▓▓▓░░▓▓    ▓  ▓▓▓       ┃
┃▓  ▓▓▓▓ ▓▓ ▓  ▓▓▓  ▓  ▓  ▓ ▓▓  ▓┃    ┃▓    ▓▓▓▓▓▓░░▓▓▓   ▓  ▓▓▓▓░     ┃
┃▓▓  ▓ ▓▓▓▓  ▓▓▓    ▓ ▓▓▓▓▓▓ ▓▓  ┃    ┃▓▓   ▓▓▓▓▓    ▓▓   ▓▓▓▓▓▓▓░░    ┃
┃ ▓▓  ▓  ▓▓▓    ▓▓  ▓▓ ▓▓    ▓  ▓┃    ┃▓▓     ▓▓▓    ░░   ▓▓▓▓▓        ┃
┃▓      ▓▓  ▓ ▓ ▓   ▓▓▓▓▓   ▓▓ ▓ ┃    ┃ ▓     ▓▓▓▓▓▓▓▓░   ▓▓▓▓▓        ┃
┃ ▓▓▓ ▓▓▓ ▓▓▓▓▓▓ ▓ ▓▓   ▓▓▓ ▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓      ┃
┃ ▓ ▓▓▓▓▓  ▓▓▓   ▓▓ ▓  ▓ ▓▓      ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓      ┃
┃▓ ▓   ▓▓▓▓   ▓ ▓▓▓       ▓▓▓▓ ▓▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓ ┃
┃   ▓ ▓ ▓  ▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓▓ ▓▓ ▓┃    ┃          ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓ ┃
┃           ▓▓▓▓▓      ▓▓   ▓ ▓▓ ┃    ┃          ▓▓▓▓▓▓▓          ▓▓▓▓ ┃
┃▓ ▓▓▓▓ ▓ ▓▓▓▓ ▓▓▓  ▓      ▓ ▓▓▓▓┃    ┃  ▓▓▓    ▓▓▓▓▓▓▓▓           ▓▓▓ ┃
┃ ▓▓▓▓  ▓▓  ▓▓▓ ▓ ▓     ▓     ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓           ▓▓▓ ┃
┃  ▓ ▓▓▓▓▓▓ ▓▓  ▓▓   ▓  ▓▓   ▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓   ▓▓▓ ┃
┃ ▓ ▓ ▓▓  ▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓ ┃
┃▓▓   ▓▓▓▓▓▓  ▓▓▓▓  ▓▓ ▓ ▓   ▓▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓   ▓▓▓ ┃
┃ ▓  ▓▓▓  ▓ ▓▓▓▓    ▓ ▓▓▓▓▓ ▓▓▓▓ ┃    ┃     ▓▓  ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓   ▓  ▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓▓┃    ┃     ▓▓  ▓▓▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓▓▓┃
┃▓   ▓▓ ▓ ▓  ▓▓ ▓▓  ▓  ▓  ▓▓▓  ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓▓  ▓▓┃
┃    ▓▓ ▓▓▓▓  ▓▓▓▓▓     ▓▓▓    ▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓    ▓ ┃
┃▓   ▓ ▓   ▓▓▓▓▓▓▓▓▓ ▓▓   ▓    ▓ ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓    ▓ ┃
┃ ▓   ▓▓▓ ▓ ▓▓▓▓   ▓ ▓▓  ▓▓▓ ▓ ▓ ┃    ┃         ▓▓▓▓▓▓     ▓▓  ▓▓    ▓ ┃
┃    ▓    ▓▓ ▓▓         ▓▓   ▓ ▓▓┃    ┃          ▓▓▓▓         ▓▓     ▓▓┃
┃     ▓ ▓  ▓  ▓   ▓ ▓ ▓ ▓  ▓  ▓▓▓┃    ┃                       ▓      ▓▓┃
┃▓     ▓    ▓▓ ▓  ▓  ▓ ▓▓    ▓   ┃    ┃                       ▓        ┃
┃▓   ▓ ▓▓   ▓  ▓ ▓  ▓▓▓ ▓  ▓ ▓  ▓┃    ┃      ▓▓           ▓▓░░▓        ┃
┃    ▓▓  ▓▓▓▓▓     ▓▓   ▓▓ ▓   ▓ ┃    ┃     ▓▓▓▓░         ▓▓░░▓▓       ┃
┃ ▓▓▓▓ ▓▓▓      ▓   ▓▓▓ ▓▓▓ ▓▓▓  ┃    ┃  ▓▓▓▓▓▓▓          ▓▓  ▓▓  ▓▓   ┃
┃▓ ▓▓▓ ▓ ▓   ▓  ▓▓▓▓   ▓▓▓  ▓▓ ▓▓┃    ┃  ▓▓▓                  ▓▓  ▓▓   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓     ▓ ▓▓▓▓▓  ▓▓▓▓  ▓  ▓ ▓▓▓▓ ┃    ┃▓▓                ▓▓       ▓▓▓  ┃
┃▓▓ ▓▓▓▓ ▓  ▓     ▓ ▓▓▓  ▓ ▓▓▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓       ▓▓▓  ┃
┃▓ ▓▓▓▓ ▓ ▓ ▓      ▓▓  ▓▓ ▓ ▓▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓       ▓▓   ┃
┃▓▓▓ ▓▓▓▓ ▓▓▓ ▓▓ ▓▓▓   ▓   ▓ ▓   ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓       ▓▓    ┃
┃ ▓      ▓▓▓▓ ▓▓ ▓▓  ▓ ▓  ▓▓    ▓┃    ┃     ▓▓▓▓▓▓▓ ▓▓▓▓▓▓      ▓▓▓    ┃
┃▓ ▓ ▓▓▓▓▓ ▓  ▓ ▓ ▓▓▓  ▓▓ ▓▓▓  ▓ ┃    ┃      ▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓▓    ┃
┃ ▓    ▓ ▓  ▓  ▓▓▓▓▓    ▓▓▓▓▓ ▓▓ ┃    ┃               ▓▓▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃▓▓  ▓▓   ▓ ▓ ▓  ▓▓▓▓  ▓▓  ▓  ▓▓▓┃    ┃               ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓ ┃
┃  ▓    ▓▓ ▓    ▓▓ ▓ ▓ ▓▓ ▓ ▓▓ ▓ ┃    ┃                ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓▓  ▓▓▓▓    ▓▓ ▓▓▓▓  ▓▓▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓   ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓▓ ▓▓  ▓ ▓▓▓▓  ▓▓ ▓  ▓▓▓▓▓▓  ┃    ┃▓▓▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓▓▓  ▓   ▓▓▓ ▓▓   ▓▓▓ ▓  ▓  ▓ ┃    ┃  ▓▓▓▓     ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃    ▓▓ ▓    ▓ ▓▓ ▓▓▓▓▓▓ ▓▓▓▓▓▓▓ ┃    ┃  ▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃  ▓▓▓▓   ▓ ▓     ▓ ▓ ▓▓ ▓ ▓ ▓▓  ┃    ┃  ▓▓▓▓     ░▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓  ┃
┃▓ ▓▓▓   ▓▓ ▓▓▓▓▓▓ ▓ ▓ ▓  ▓▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓     ▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓  ┃
┃ ▓▓▓▓▓▓▓ ▓ ▓ ▓▓    ▓▓ ▓  ▓▓ ▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓  ▓▓▓▓▓  ┃
┃ ▓ ▓▓▓▓▓  ▓▓   ▓  ▓  ▓▓▓▓ ▓▓   ▓┃    ┃ ▓▓▓▓▓▓▓      ▓▓   ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓▓ ▓▓▓▓  ▓  ▓▓  ▓▓▓ ▓▓  ▓▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓      ▓▓   ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓    ▓▓▓      ▓ ▓▓  ▓ ▓▓▓▓▓▓▓▓  ┃    ┃▓▓   ▓▓▓      ▓▓     ▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓ ▓▓   ▓   ▓▓  ▓  ▓   ▓▓▓▓▓ ▓ ┃    ┃▓▓   ▓▓                 ▓▓▓▓▓▓  ┃
┃ ▓   ▓▓  ▓  ▓     ▓   ▓   ▓ ▓▓▓▓┃    ┃    ▓▓▓                 ▓▓▓▓▓▓▓▓┃
┃   ▓▓ ▓  ▓▓  ▓ ▓▓  ▓▓▓▓▓▓▓ ▓▓  ▓┃    ┃   ▓▓▓       ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓▓    ▓   ▓▓▓▓▓  ▓  ▓ ▓▓▓▓▓▓▓┃    ┃   ▓▓        ▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓   ▓     ▓▓  ▓▓▓▓▓  ▓▓▓  ▓ ▓▓  ┃    ┃    ▓    ▓▓  ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓  ▓   ▓▓▓ ▓▓ ▓  ▓▓    ▓ ▓   ▓ ┃    ┃    ▓    ▓▓▓▓▓▓▓▓▓▓▓     ░░     ┃
┃  ▓▓▓ ▓    ▓ ▓▓▓ ▓ ▓ ▓▓  ▓      ┃    ┃   ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ░░     ┃
┃  ▓ ▓▓ ▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓  ▓  ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓  ░░     ┃
┃▓   ▓▓ ▓▓▓ ▓▓▓▓  ▓ ▓▓▓  ▓▓▓▓  ▓ ┃    ┃    ▓▓▓▓▓▓▓░▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓  ▓ ▓  ▓ ▓ ▓▓▓▓ ▓▓ ▓  ▓▓  ▓▓▓▓ ┃    ┃       ▓▓▓░░▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓ ┃
┃ ▓     ▓▓ ▓▓ ▓▓▓ ▓▓▓   ▓ ▓ ▓ ▓▓▓┃    ┃       ▓▓▓░░▓▓▓▓▓▓▓▓       ▓▓▓▓ ┃
┃  ▓▓   ▓▓     ▓▓▓▓▓     ▓  ▓ ▓▓ ┃    ┃       ▓▓   ▓▓▓▓▓▓▓▓       ▓▓▓▓ ┃
┃▓  ▓ ▓  ▓▓ ▓▓▓   ▓ ▓▓▓  ▓ ▓▓▓   ┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓   ▓▓ ▓ ▓▓ ▓     ▓▓  ▓ ▓  ▓  ┃    ┃          ▓▓▓                   ┃
┃▓▓     ▓ ▓▓▓▓   ▓  ▓▓  ▓  ▓▓  ▓ ┃    ┃          ▓▓▓       ▓▓          ┃
┃▓ ▓▓▓▓▓ ▓  ▓▓  ▓▓ ▓ ▓▓▓       ▓▓┃    ┃    ▓▓▓▓   ▓▓   ▓▓▓▓▓▓▓         ┃
┃ ▓  ▓ ▓▓▓  ▓▓▓  ▓▓▓   ▓  ▓    ▓ ┃    ┃    ▓▓▓▓   ▓▓   ▓▓▓▓▓▓▓         ┃
┃    ▓      ▓▓   ▓  ▓ ▓▓ ▓▓ ▓ ▓▓▓┃    ┃    ▓      ▓▓   ▓▓▓▓▓▓▓▓        ┃
┃   ▓▓   ▓  ▓ ▓▓▓▓▓▓ ▓ ▓▓ ▓ ▓    ┃    ┃    ▓      ▓▓░░░▓▓▓▓▓▓▓▓        ┃
┃  ▓ ▓▓▓  ▓ ▓    ▓ ▓ ▓ ▓▓   ▓ ▓  ┃    ┃    ▓▓   ▓▓▓▓░░░▓▓▓▓▓▓▓▓        ┃
┃▓   ▓▓  ▓▓▓▓▓▓▓▓ ▓ ▓▓▓▓  ▓▓▓▓  ▓┃    ┃    ▓▓   ▓▓▓▓░░░▓▓▓▓▓▓▓▓ ▓▓▓    ┃
┃ ▓    ▓ ▓ ▓  ▓    ▓ ▓▓ ▓ ▓▓▓   ▓┃    ┃           ░░░     ▓▓▓▓  ▓▓▓▓   ┃
┃▓▓ ▓       ▓ ▓  ▓ ▓ ▓     ▓ ▓ ▓ ┃    ┃▓▓          ░░     ░░     ▓▓▓   ┃
┃▓▓  ▓▓▓▓▓▓  ▓  ▓ ▓ ▓   ▓  ▓▓▓▓  ┃    ┃▓▓  ▓▓▓▓    ░░     ░░     ▓▓▓   ┃
┃▓  ▓ ▓▓ ▓ ▓▓▓▓▓ ▓  ▓▓▓▓ ▓  ▓▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓▓▓    ▓▓▓  ┃
┃▓▓  ▓▓▓▓    ▓▓  ▓ ▓ ▓▓▓  ▓  ▓   ┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓     ▓▓  ┃
┃▓▓▓▓▓ ▓▓▓▓   ▓▓▓   ▓    ▓   ▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓          ▓▓  ┃
┃ ▓   ▓   ▓     ▓▓▓▓▓  ▓ ▓  ▓▓▓▓▓┃    ┃     ▓▓▓▓▓     ▓▓▓          ▓▓  ┃
┃▓   ▓▓▓▓▓ ▓▓▓   ▓ ▓  ▓  ▓  ▓    ┃    ┃     ▓▓▓▓▓▓▓   ▓▓▓              ┃
┃▓    ▓ ▓ ▓▓▓  ▓▓▓      ▓  ▓  ▓  ┃    ┃     ▓▓▓▓▓▓▓  ▓▓▓               ┃
┃  ▓  ▓ ▓ ▓▓   ▓ ▓▓     ▓  ▓     ┃    ┃     ▓▓▓▓▓▓▓  ▓▓▓               ┃
┃▓▓▓ ▓▓  ▓ ▓ ▓▓▓ ▓  ▓   ▓ ▓  ▓ ▓ ┃    ┃     ▓  ░░   ▓▓▓▓      ▓▓       ┃
┃      ▓▓   ▓  ▓▓▓   ▓  ▓▓ ▓▓ ▓▓ ┃    ┃     ▓  ░░   ▓▓▓▓      ▓▓       ┃
┃  ▓▓▓▓  ▓▓   ▓  ▓▓▓▓   ▓▓▓ ▓  ▓▓┃    ┃    ▓▓  ▓▓   ▓▓▓▓▓     ▓▓  ▓▓▓▓▓┃
┃▓▓  ▓▓  ▓▓ ▓ ▓▓▓    ▓▓▓   ▓ ▓▓▓▓┃    ┃    ▓▓  ▓▓  ▓▓▓▓▓▓         ▓▓▓▓▓┃
┃ ▓▓    ▓   ▓▓ ▓▓▓▓ ▓▓   ▓  ▓▓ ▓ ┃    ┃        ▓  ▓▓▓▓▓▓▓░        ▓▓▓▓ ┃
┃   ▓    ▓▓  ▓  ▓ ▓▓ ▓    ▓ ▓ ▓  ┃    ┃       ▓▓  ▓▓   ▓▓░░      ▓▓▓▓▓ ┃
┃ ▓  ▓▓▓▓▓ ▓▓▓      ▓ ▓▓▓ ▓▓▓▓▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓            ▓▓▓▓▓  ┃
┃   ▓ ▓▓ ▓ ▓  ▓      ▓   ▓   ▓▓ ▓┃    ┃     ▓▓▓▓▓▓▓▓            ▓▓▓▓▓  ┃
┃ ▓▓▓▓ ▓ ▓▓▓▓▓        ▓   ▓▓ ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓        ░    ▓▓▓▓▓  ┃
┃▓ ▓▓ ▓ ▓  ▓   ▓ ▓▓ ▓▓  ▓ ▓▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓         ░░  ▓▓▓▓▓░▓▓┃
┃ ▓  ▓   ▓▓▓ ▓▓▓▓   ▓ ▓ ▓▓▓▓ ▓▓▓▓┃    ┃ ▓▓▓▓  ▓▓▓▓ ▓▓     ▓▓▓▓▓▓▓▓▓░░▓▓┃
┃ ▓▓▓▓ ▓▓ ▓  ▓ ▓    ▓▓▓▓▓▓ ▓▓   ▓┃    ┃ ▓▓▓▓  ▓▓▓▓ ▓▓     ▓▓▓▓▓▓▓▓     ┃
┃ ▓   ▓ ▓ ▓▓ ▓▓  ▓   ▓▓ ▓▓▓▓  ▓ ▓┃    ┃ ▓▓                 ▓▓▓▓▓▓▓     ┃
┃▓▓▓   ▓     ▓ ▓ ▓   ▓  ▓     ▓  ┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓▓ ▓ ▓▓▓▓▓▓▓   ▓ ▓▓ ▓  ▓ ▓▓▓▓▓┃    ┃        ▓▓▓▓▓▓             ▓▓▓▓▓┃
┃▓ ▓   ▓ ▓▓▓▓ ▓ ▓  ▓     ▓  ▓ ▓▓▓┃    ┃ ▓▓▓    ▓▓▓▓▓▓             ▓▓▓▓▓┃
┃ ▓▓▓▓  ▓▓▓ ▓ ▓ ▓    ▓▓▓    ▓▓ ▓▓┃    ┃ ▓▓▓    ▓▓▓▓▓▓      ▓▓▓     ▓▓▓▓┃
┃ ▓   ▓▓  ▓ ▓▓▓      ▓ ▓▓▓▓▓    ▓┃    ┃           ▓▓▓      ▓▓▓▓▓       ┃
┃▓  ▓       ▓▓▓▓▓▓▓  ▓▓▓ ▓ ▓    ▓┃    ┃           ▓▓▓▓▓▓▓  ▓▓▓▓▓       ┃
┃     ▓    ▓▓ ▓▓▓▓▓ ▓▓▓▓▓    ▓   ┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓ ▓▓ ▓    ▓ ▓   ▓▓▓▓     ▓     ▓┃    ┃ ▓▓       ▓▓▓   ▓▓▓▓▓▓▓         ┃
┃▓▓▓  ▓▓▓ ▓▓▓      ▓▓ ▓▓ ▓▓▓▓  ▓ ┃    ┃▓▓▓   ▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓      ┃
┃▓     ▓▓▓  ▓▓ ▓ ▓▓▓▓▓▓▓▓▓  ▓ ▓ ▓┃    ┃▓▓    ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓  ░   ┃
┃▓▓▓     ▓▓▓ ▓▓▓  ▓▓▓▓  ▓ ▓  ▓▓▓▓┃    ┃▓▓      ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓  ▓▓▓▓▓┃
┃▓▓   ▓    ▓ ▓▓▓  ▓   ▓ ▓   ▓ ▓▓▓┃    ┃▓▓▓         ▓▓▓            ▓▓▓▓▓┃
┃ ▓▓    ▓    ▓▓   ▓     ▓   ▓▓   ┃    ┃ ▓▓         ▓▓             ▓▓   ┃
┃  ▓  ▓  ▓ ▓ ▓   ▓  ▓▓ ▓▓▓   ▓ ▓ ┃    ┃ ░░      ▓▓▓▓              ▓    ┃
┃ ▓ ▓ ▓ ▓▓▓▓▓▓  ▓▓  ▓      ▓▓   ▓┃    ┃ ░░     ▓▓▓▓▓      ▓▓     ▓▓    ┃
┃▓ ▓▓ ▓▓  ▓▓▓▓▓   ▓ ▓▓▓ ▓▓ ▓▓    ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓    ▓▓▓    ┃
┃ ▓  ▓▓ ▓            ▓  ▓ ▓ ▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓░         ░░▓▓▓▓▓▓▓▓ ┃
┃  ▓▓ ▓ ▓▓▓▓▓▓ ▓▓ ▓ ▓ ▓ ▓  ▓▓ ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓          ░▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓  ▓   ▓▓    ▓▓ ▓ ▓▓ ▓▓▓▓▓   ┃    ┃ ▓▓▓▓▓▓  ▓▓▓   ▓▓      ▓▓▓▓▓▓   ┃
┃ ▓▓ ▓▓  ▓▓▓ ▓ ▓▓▓   ▓   ▓▓ ▓▓  ▓┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓  ▓▓       ▓▓▓▓▓   ┃
┃▓▓ ▓ ▓▓    ▓▓  ▓▓         ▓ ▓▓▓▓┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓        ▓▓▓▓▓  ┃
┃▓     ▓▓▓ ▓▓  ▓▓▓▓▓▓ ▓ ▓ ▓▓▓ ▓  ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓  ┃
┃ ▓ ▓▓ ▓▓▓▓▓ ▓▓▓ ▓▓▓ ▓ ▓▓ ▓  ▓▓  ┃    ┃      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓  ┃
┃▓ ▓▓        ▓ ▓▓▓    ▓ ▓     ▓▓▓┃    ┃             ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓┃
┃   ▓  ▓ ▓  ▓  ▓▓▓▓▓▓▓▓ ▓▓ ▓▓▓  ▓┃    ┃              ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓  ▓▓ ▓▓ ▓▓ ▓▓▓▓     ▓▓▓▓ ▓▓▓ ▓┃    ┃              ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓  ▓ ▓▓    ▓ ▓   ▓▓▓▓   ▓ ▓▓▓┃    ┃▓▓▓▓▓░░░      ░░    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓ ▓▓▓ ▓    ▓▓   ▓ ▓▓▓ ▓▓▓▓▓  ▓▓┃    ┃▓▓▓▓▓░░░░     ░░    ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓     ▓▓▓▓▓▓ ▓ ▓   ▓▓▓ ▓▓ ▓ ▓  ┃    ┃▓▓     ░▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃         ▓▓▓ ▓▓ ▓  ▓▓▓▓▓  ▓ ▓▓ ▓┃    ┃       ░▓▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓▓▓ ┃
┃▓▓  ▓ ▓ ▓▓▓ ▓  ▓▓ ▓  ▓   ▓   ▓▓▓┃    ┃▓▓     ░▓▓▓▓  ▓▓▓   ▓▓▓     ▓▓▓▓┃
┃▓▓▓▓ ▓▓▓ ▓▓▓  ▓▓    ▓▓▓▓▓▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓  ▓▓▓▓         ▓▓     ▓▓▓▓┃
┃▓  ▓▓▓  ▓ ▓▓   ▓ ▓ ▓        ▓▓▓▓┃    ┃   ▓▓▓   ▓▓▓                ▓▓▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃   ▓▓    ▓▓ ▓ ▓ ▓▓▓ ▓▓▓▓ ▓▓    ▓┃    ┃         ▓▓▓▓░      ▓▓▓         ┃
┃ ▓▓▓ ▓   ▓▓▓▓▓▓▓ ▓  ▓▓      ▓ ▓▓┃    ┃         ▓▓▓▓       ▓▓▓         ┃
┃     ▓ ▓        ▓     ▓  ▓ ▓▓▓  ┃    ┃                           ▓▓▓  ┃
┃      ▓ ▓ ▓▓▓ ▓ ▓ ▓▓  ▓    ▓ ▓ ▓┃    ┃         ░▓▓▓▓▓▓▓          ▓▓▓  ┃
┃  ▓ ▓▓   ▓▓▓▓▓ ▓▓   ▓▓  ▓▓ ▓▓▓  ┃    ┃    ▓▓▓░░░▓▓▓▓▓▓▓  ▓▓▓  ▓▓▓▓▓▓  ┃
┃  ▓ ▓▓▓ ▓ ▓ ▓▓▓▓▓  ▓▓▓ ▓▓▓▓   ▓▓┃    ┃   ▓▓▓▓░░░▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓ ▓ ▓  ▓  ▓▓▓▓ ▓▓▓▓ ▓▓  ▓ ▓▓  ┃    ┃ ▓▓▓▓▓▓░░░▓▓▓▓▓▓▓  ▓▓▓▓   ▓▓    ┃
┃ ▓ ▓▓  ▓▓▓▓  ▓▓     ▓▓ ▓  ▓▓   ▓┃    ┃ ▓▓▓▓▓▓      ▓▓    ▓▓▓▓   ▓▓    ┃
┃ ▓▓▓ ▓▓  ▓    ▓    ▓▓▓▓  ▓▓  ▓  ┃    ┃ ▓▓▓▓▓▓      ▓▓    ▓▓▓▓  ▓▓▓    ┃
┃  ▓  ▓▓ ▓  ▓▓▓▓ ▓  ▓  ▓  ▓▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓▓    ▓▓▓▓    ▓  ▓  ▓▓▓▓▓  ┃
┃▓▓▓▓     ▓ ▓▓  ▓▓▓▓▓  ▓▓    ▓ ▓▓┃    ┃ ▓▓        ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓ ┃
┃    ▓  ▓ ▓ ▓▓ ▓  ▓▓▓▓ ▓▓▓▓ ▓▓▓▓ ┃    ┃           ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓  ▓▓▓▓     ▓▓  ▓   ▓▓ ▓▓▓    ┃    ┃     ▓▓▓▓▓    ▓▓▓▓    ▓▓▓▓▓▓    ┃
┃▓▓▓ ▓ ▓▓▓▓▓ ▓▓ ▓▓▓   ▓▓▓▓ ▓▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓    ▓▓▓▓▓▓  ▓▓┃
┃▓▓▓ ▓ ▓   ▓▓   ▓▓▓ ▓  ▓       ▓▓┃    ┃▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓   ▓▓▓    ▓▓▓┃
┃  ▓ ▓▓    ▓▓▓ ▓  ▓▓▓ ▓ ▓▓ ▓ ▓▓  ┃    ┃   ▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓▓▓    ▓▓ ┃
┃▓▓ ▓▓▓▓     ▓▓   ▓▓  ▓▓▓▓  ▓ ▓▓▓┃    ┃    ▓▓▓    ▓▓    ▓▓▓▓▓▓▓▓    ▓▓ ┃
┃  ▓   ▓   ▓▓  ▓ ▓▓▓▓▓ ▓  ▓▓▓  ▓ ┃    ┃                 ▓▓▓▓▓▓▓▓▓      ┃
┃   ▓▓   ▓     ▓  ▓▓ ▓  ▓▓  ▓▓   ┃    ┃                 ▓▓▓▓▓▓▓▓▓      ┃
┃▓▓   ▓ ▓▓ ▓▓  ▓▓ ▓▓▓▓▓▓▓ ▓    ▓ ┃    ┃        ▓▓▓      ▓▓▓▓▓▓▓        ┃
┃   ▓▓▓  ▓▓▓  ▓   ▓ ▓ ▓   ▓      ┃    ┃    ▓▓▓▓▓▓▓         ░           ┃
┃  ▓  ▓▓▓ ▓▓▓ ▓ ▓▓ ▓   ▓▓        ┃    ┃    ▓▓▓▓▓▓▓  ▓▓                 ┃
┃ ▓ ▓▓▓▓▓ ▓▓  ▓▓ ▓ ▓ ▓  ▓  ▓     ┃    ┃    ▓▓▓▓▓▓▓  ▓▓                 ┃
┃▓ ▓ ▓ ▓ ▓ ▓   ▓   ▓ ▓     ▓▓ ▓▓▓┃    ┃    ▓▓▓▓▓▓▓  ▓▓            ▓▓▓▓ ┃
┃▓     ▓▓ ▓▓  ▓▓ ▓   ▓    ▓▓ ▓▓ ▓┃    ┃      ▓▓▓    ▓▓            ▓▓▓▓ ┃
┃▓▓   ▓ ▓     ▓     ▓ ▓  ▓   ▓   ┃    ┃      ▓▓                    ▓▓  ┃
┃▓  ▓  ▓▓  ▓▓   ▓▓▓▓    ▓    ▓ ▓▓┃    ┃      ▓▓  ▓▓    ▓▓▓         ▓▓  ┃
┃ ▓    ▓ ▓▓▓▓ ▓ ▓  ▓  ▓▓   ▓ ▓▓  ┃    ┃          ▓▓    ▓▓▓             ┃
┃▓  ▓▓  ▓   ▓ ▓  ▓▓▓   ▓    ▓▓ ▓▓┃    ┃                 ▓▓             ┃
┃▓  ▓ ▓ ▓▓   ▓     ▓  ▓▓ ▓   ▓   ┃    ┃       ░                        ┃
┃  ▓ ▓▓ ▓ ▓ ▓▓ ▓▓▓  ▓  ▓     ▓   ┃    ┃       ▓▓▓▓▓▓▓▓▓▓               ┃
┃▓▓▓▓ ▓ ▓▓▓▓▓ ▓▓▓▓    ▓ ▓▓▓   ▓▓▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓               ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓▓▓▓▓  ▓▓  ▓▓ ▓▓▓▓▓▓       ▓▓┃    ┃     ▓▓▓  ▓▓     ▓▓▓▓▓▓         ┃
┃ ▓▓ ▓ ▓▓▓ ▓▓ ▓ ▓ ▓▓▓ ▓▓ ▓▓▓▓▓ ▓ ┃    ┃    ▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓ ▓▓▓▓▓   ┃
┃  ▓▓ ▓▓▓▓▓▓▓  ▓▓ ▓    ▓ ▓▓  ▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓            ▓▓▓▓▓   ┃
┃▓▓▓ ▓ ▓  ▓ ▓   ▓   ▓      ▓▓  ▓ ┃    ┃ ▓▓▓▓▓░                   ▓▓▓   ┃
┃ ▓▓▓ ▓▓       ▓   ▓▓    ▓ ▓ ▓▓ ▓┃    ┃ ▓▓▓▓░░                         ┃
┃▓▓ ▓  ▓ ▓ ▓     ▓      ▓▓ ▓    ▓┃    ┃ ▓▓▓▓▓░                         ┃
┃ ▓▓ ▓▓ ▓▓ ▓▓▓ ▓▓▓▓      ▓▓   ▓  ┃    ┃ ▓▓▓▓▓▓   ▓▓▓                   ┃
┃  ▓▓ ▓  ▓ ▓▓▓      ▓▓      ▓▓▓▓ ┃    ┃ ░░░▓▓▓   ▓▓▓              ▓▓▓  ┃
┃▓ ▓ ▓▓▓▓  ▓   ▓     ▓▓     ▓▓▓ ▓┃    ┃ ░░░░▓▓▓           ▓▓      ▓▓▓▓ ┃
┃ ▓ ▓ ▓▓  ▓  ▓  ▓  ▓▓▓ ▓ ▓▓  ▓▓▓▓┃    ┃  ░░░▓▓▓           ▓▓      ▓▓▓▓ ┃
┃ ▓▓ ▓▓ ▓   ▓▓  ▓   ▓  ▓    ▓    ┃    ┃   ░░▓▓▓            ▓▓          ┃
┃▓ ▓   ▓▓▓▓▓         ▓▓ ▓  ▓    ▓┃    ┃     ▓▓▓▓           ▓▓          ┃
┃▓    ▓▓▓   ▓▓▓  ▓ ▓ ▓▓ ▓ ▓▓ ▓ ▓ ┃    ┃     ▓▓▓▓   ▓▓      ▓▓▓▓▓       ┃
┃▓   ▓▓  ▓▓  ▓▓ ▓▓    ▓ ▓▓  ▓ ▓ ▓┃    ┃     ▓▓▓▓   ▓▓▓        ▓▓       ┃
┃  ▓ ▓ ▓ ▓ ▓ ▓ ▓ ▓ ▓▓   ▓▓▓ ▓▓ ▓▓┃    ┃     ░░░░   ▓▓▓▓  ▓▓   ▓▓    ░  ┃
┃ ▓▓▓ ▓▓▓  ▓ ▓ ▓   ▓▓▓  ▓   ▓ ▓▓ ┃    ┃      ░░░   ▓▓▓▓  ▓▓▓  ░░  ▓▓▓▓ ┃
┃▓ ▓ ▓  ▓▓    ▓▓▓ ▓ ▓▓   ▓▓ ▓▓   ┃    ┃ ▓▓▓▓  ░░   ▓▓▓▓░░▓▓▓  ░░  ▓▓▓▓ ┃
┃▓ ▓▓▓  ▓ ▓ ▓▓▓▓▓▓ ▓▓▓  ▓    ▓▓▓ ┃    ┃▓▓▓▓▓  ░░░░░▓▓▓▓░░▓▓▓  ░░  ▓▓▓▓ ┃
┃▓▓▓ ▓▓  ▓ ▓▓  ▓    ▓ ▓▓▓▓▓▓▓ ▓▓ ┃    ┃▓▓▓▓▓  ░░░░░      ░░░░░▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓  ▓▓ ▓     ▓  ▓ ▓   ▓▓▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓░░░░      ░░░░░▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓ ▓▓▓  ▓▓▓▓▓▓ ▓▓▓▓▓▓▓    ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓   ▓▓▓▓   ▓▓▓▓     ░    ┃
┃▓▓ ▓▓▓  ▓  ▓ ▓      ▓      ▓ ▓  ┃    ┃ ▓▓▓▓▓▓    ▓▓▓▓   ▓▓▓▓          ┃
┃ ▓    ▓    ▓ ▓ ▓ ▓▓▓▓ ▓▓ ▓▓   ▓▓┃    ┃ ▓▓▓▓▓▓    ▓▓▓▓░▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓ ▓▓ ▓▓▓▓▓▓ ▓ ▓▓▓▓ ▓▓ ▓▓▓ ▓▓▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃  ▓▓▓▓▓▓▓ ▓ ▓▓   ▓ ▓▓▓ ▓ ▓▓▓   ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓ ▓▓▓  ▓ ▓▓ ▓ ▓▓▓     ▓▓  ▓  ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓       ┃
┃▓▓ ▓   ▓▓▓   ▓▓ ▓▓▓  ▓  ▓   ▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓  ▓▓▓▓▓┃
┃ ▓▓ ▓ ▓▓▓ ▓ ▓▓▓   ▓ ▓   ▓ ▓▓▓  ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓     ▓▓▓▓▓▓▓▓┃
┃▓   ▓▓ ▓▓▓▓▓ ▓   ▓▓ ▓ ▓ ▓▓▓▓ ▓▓ ┃    ┃       ▓▓▓▓      ▓▓     ▓▓▓▓▓▓▓ ┃
┃  ▓   ▓  ▓▓ ▓  ▓ ▓▓▓ ▓   ▓▓ ▓▓ ▓┃    ┃       ▓▓▓▓      ▓▓      ▓▓▓▓▓▓ ┃
┃▓ ▓▓▓  ▓ ▓    ▓▓▓    ▓   ▓▓▓ ▓ ▓┃    ┃  ▓▓          ▓▓         ▓▓▓▓▓▓ ┃
┃ ▓▓▓  ▓   ▓   ▓▓   ▓▓ ▓ ▓▓▓ ▓▓▓ ┃    ┃  ▓▓          ▓▓         ▓▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓▓▓ ▓  ▓▓   ▓  ▓ ▓  ▓▓▓▓ ▓  ▓ ┃    ┃▓▓▓▓▓    ▓▓                     ┃
┃▓▓▓ ▓▓ ▓▓▓▓▓    ▓▓▓▓▓ ▓  ▓ ▓    ┃    ┃▓▓▓▓▓  ▓▓▓▓▓                    ┃
┃  ▓   ▓▓▓▓▓▓ ▓▓▓    ▓▓ ▓   ▓   ▓┃    ┃       ▓▓▓▓▓░░▓▓      ░         ┃
┃▓      ▓    ▓ ▓▓ ▓    ▓▓▓   ▓ ▓ ┃    ┃         ░░░░░▓▓     ▓▓▓▓       ┃
┃▓ ▓  ▓   ▓▓▓   ▓  ▓  ▓▓▓▓  ▓▓▓  ┃    ┃         ░░░░░       ▓▓▓▓  ▓▓▓  ┃
┃▓▓  ▓ ▓ ▓▓  ▓▓ ▓▓  ▓ ▓ ▓  ▓▓▓▓  ┃    ┃      ▓▓▓▓  ▓▓       ▓▓▓▓  ▓▓▓  ┃
┃▓ ▓▓  ▓▓▓   ▓▓       ▓ ▓▓▓ ▓▓▓  ┃    ┃  ▓▓  ▓▓▓▓  ▓▓       ▓▓▓▓▓▓▓▓▓  ┃
┃  ▓▓▓ ▓ ▓ ▓▓▓    ▓  ▓ ▓▓ ▓ ▓▓   ┃    ┃  ▓▓  ▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓    ▓▓▓ ▓▓ ▓▓ ▓▓ ▓▓ ▓   ▓▓ ▓▓ ┃    ┃  ▓▓  ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃ ▓▓▓▓ ▓ ▓▓      ▓  ▓▓▓▓▓▓▓ ▓    ┃    ┃  ▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓  ▓▓ ▓ ▓ ▓ ▓▓ ▓▓▓ ▓▓ ▓▓ ▓▓▓▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓ ▓▓▓ ▓▓▓   ▓▓▓ ▓▓      ▓   ▓▓┃    ┃  ▓▓▓▓▓▓▓▓     ▓▓▓      ▓▓    ▓▓┃
┃ ▓▓▓  ▓ ▓    ▓ ▓      ▓▓▓▓     ▓┃    ┃     ▓▓▓▓▓              ▓▓    ▓▓┃
┃     ▓▓▓▓▓▓   ▓▓  ▓▓     ▓   ▓ ▓┃    ┃     ▓▓▓▓▓        ▓▓    ▓▓    ▓▓┃
┃ ▓▓  ▓▓▓▓▓  ▓  ▓  ▓▓   ▓▓▓▓▓▓▓▓▓┃    ┃ ▓▓  ▓▓▓▓▓        ▓▓    ▓▓▓▓▓▓▓▓┃
┃ ▓▓▓   ▓ ▓▓  ▓ ▓  ▓  ▓    ▓▓  ▓▓┃    ┃ ▓▓    ▓▓▓              ▓▓▓▓▓▓▓▓┃
┃▓▓▓  ▓  ▓▓  ▓▓ ▓    ▓▓▓▓▓▓▓ ▓▓  ┃    ┃ ▓▓                 ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓ ▓▓▓▓ ▓ ▓ ▓  ▓▓▓▓▓  ▓▓▓▓ ▓▓▓▓┃    ┃ ▓▓               ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓   ▓   ▓ ▓    ▓▓▓▓  ▓ ▓▓   ┃    ┃▓▓▓               ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓  ▓  ▓ ▓▓    ▓ ▓▓  ▓▓▓▓   ▓▓  ┃    ┃▓▓  ░             ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃   ▓▓▓     ▓▓ ▓   ▓▓    ▓▓ ▓ ▓▓ ┃    ┃   ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓  ┃
┃  ▓▓ ▓▓▓▓▓ ▓▓▓▓▓▓▓ ▓ ▓▓   ▓▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓    ░▓    ┃
┃ ▓▓▓   ▓▓▓    ▓ ▓▓▓ ▓▓  ▓  ▓    ┃    ┃  ▓▓   ▓▓▓     ▓▓▓▓▓▓▓    ▓▓    ┃
┃    ▓  ▓▓      ▓ ▓▓▓▓▓ ▓▓▓▓▓▓  ▓┃    ┃       ▓▓       ▓▓▓▓▓▓  ▓▓▓▓    ┃
┃▓ ▓  ▓  ▓    ▓ ▓ ▓▓▓ ▓  ▓▓     ▓┃    ┃                 ▓▓▓▓▓  ▓▓▓▓    ┃
┃▓▓ ▓▓    ▓▓ ▓▓    ▓   ▓▓  ▓ ▓   ┃    ┃ ▓▓▓▓   ▓▓▓       ▓▓▓   ▓▓▓▓    ┃
┃ ▓▓▓ ▓▓ ▓▓ ▓   ▓▓ ▓▓ ▓  ▓ ▓▓▓   ┃    ┃ ▓▓▓▓▓  ▓▓▓▓            ▓▓▓▓▓   ┃
┃ ▓ ▓ ▓  ▓▓ ▓▓ ▓ ▓    ▓ ▓▓▓ ▓▓▓  ┃    ┃  ▓▓▓▓  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓   ┃
┃▓  ▓ ▓  ▓▓  ▓▓▓ ▓▓▓▓   ▓▓   ▓ ▓ ┃    ┃   ▓▓▓  ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓  ┃
┃  ▓▓▓▓  ▓  ▓  ▓▓    ▓ ▓  ▓ ▓▓ ▓▓┃    ┃   ▓▓▓       ▓▓▓       ▓▓  ▓▓▓▓ ┃
┃ ▓ ▓ ▓▓  ▓   ▓ ▓ ▓▓ ▓▓ ▓▓  ▓▓▓▓ ┃    ┃   ▓▓▓▓       ▓▓    ▓▓     ▓▓▓▓ ┃
┃▓  ▓▓ ▓▓ ▓▓▓▓  ▓   ▓▓▓       ▓  ┃    ┃    ▓▓▓             ▓▓          ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓  ▓▓▓ ▓▓   ▓▓▓▓ ▓ ▓  ▓   ▓ ▓┃    ┃       ▓▓                       ┃
┃▓    ▓ ▓▓   ▓ ▓  ▓ ▓▓ ▓▓▓▓▓  ▓  ┃    ┃       ▓▓          ▓▓▓▓▓▓▓      ┃
┃       ▓ ▓▓▓   ▓▓  ▓▓▓ ▓▓   ▓ ▓ ┃    ┃       ▓▓▓▓▓       ▓▓▓▓▓▓▓      ┃
┃ ▓▓ ▓ ▓ ▓▓▓▓   ▓   ▓  ▓  ▓▓  ▓ ▓┃    ┃       ▓▓▓▓▓       ▓▓▓▓▓▓▓      ┃
┃  ▓  ▓ ▓  ▓▓ ▓     ▓▓▓ ▓▓▓    ▓ ┃    ┃          ▓▓       ▓▓▓▓▓▓▓      ┃
┃▓  ▓   ▓  ▓▓        ▓ ▓  ▓   ▓▓▓┃    ┃          ▓▓                 ▓▓ ┃
┃  ▓   ▓▓ ▓▓ ▓▓  ▓ ▓ ▓▓     ▓▓▓▓ ┃    ┃          ▓▓▓              ▓▓▓▓ ┃
┃▓ ▓   ▓    ▓ ▓ ▓      ▓   ▓▓ ▓  ┃    ┃ ▓▓       ▓▓▓▓            ▓▓▓▓▓ ┃
┃▓▓▓▓ ▓  ▓▓▓▓ ▓    ▓      ▓▓▓▓ ▓ ┃    ┃ ▓▓▓▓     ▓▓▓▓            ▓▓▓▓▓ ┃
┃   ▓▓  ▓ ▓  ▓▓▓▓  ▓  ▓   ▓  ▓▓▓▓┃    ┃   ▓▓▓    ▓▓▓▓▓▓          ▓▓▓▓▓▓┃
┃    ▓▓▓ ▓  ▓▓▓▓▓ ▓▓ ▓▓  ▓ ▓  ▓ ▓┃    ┃   ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓┃
┃   ▓ ▓▓▓▓▓▓  ▓  ▓▓▓▓ ▓   ▓▓ ▓▓ ▓┃    ┃   ▓▓▓▓▓▓▓       ▓▓▓     ▓▓▓▓▓▓ ┃
┃  ▓  ▓ ▓▓ ▓   ▓    ▓▓ ▓   ▓▓ ▓▓ ┃    ┃   ▓▓▓▓▓▓▓       ▓▓▓     ▓▓▓▓▓  ┃
┃▓  ▓ ▓▓▓▓  ▓▓  ▓ ▓▓   ▓ ▓▓▓▓▓▓  ┃    ┃   ▓▓▓▓▓▓▓▓             ▓▓▓▓▓▓  ┃
┃▓ ▓▓   ▓ ▓▓    ▓ ▓  ▓▓ ▓▓▓▓  ▓  ┃    ┃        ▓▓▓▓            ▓▓▓  ▓  ┃
┃▓ ▓ ▓   ▓▓▓▓▓ ▓▓ ▓      ▓    ▓▓ ┃    ┃   ░    ▓▓▓▓  ▓▓▓            ▓▓ ┃
┃▓  ▓ ▓  ▓ ▓   ▓▓▓  ▓▓▓      ▓▓▓ ┃    ┃        ▓▓    ▓▓▓▓           ▓▓ ┃
┃  ▓ ▓ ▓ ▓   ▓  ▓ ▓▓ ▓ ▓ ▓▓▓    ▓┃    ┃        ▓▓     ▓▓▓▓    ▓▓▓▓  ▓▓ ┃
┃ ▓▓▓▓  ▓▓▓▓    ▓▓▓▓▓  ▓▓ ▓▓ ▓▓▓ ┃    ┃               ▓▓▓▓    ▓▓▓▓▓▓▓▓ ┃
┃   ▓       ▓▓ ▓▓  ▓    ▓  ▓▓ ▓▓ ┃    ┃               ▓▓▓▓░   ▓  ▓▓▓▓▓ ┃
┃▓  ▓   ▓ ▓     ▓▓  ▓   ▓   ▓▓   ┃    ┃              ▓▓▓▓▓    ▓  ▓▓    ┃
┃▓▓ ▓ ▓▓▓▓▓ ▓  ▓▓▓▓▓  ▓ ▓▓▓▓▓  ▓▓┃    ┃   ▓▓▓▓       ▓▓▓▓     ▓▓▓▓▓    ┃
┃  ▓ ▓▓ ▓   ▓ ▓▓▓▓▓ ▓▓ ▓    ▓  ▓ ┃    ┃  ▓▓▓▓▓      ▓▓▓▓▓     ░░       ┃
┃ ▓  ▓    ▓ ▓▓ ▓▓    ▓▓ ▓▓ ▓  ▓ ▓┃    ┃ ▓▓▓▓     ▓▓▓▓▓▓▓      ░░       ┃
┃▓▓▓▓▓ ▓ ▓▓▓   ▓  ▓▓ ▓   ▓ ▓ ▓▓▓▓┃    ┃▓▓▓▓▓    ▓▓▓▓▓▓▓▓      ▓▓▓░░    ┃
┃▓▓  ▓    ▓▓ ▓▓▓▓ ▓    ▓▓▓▓ ▓ ▓  ┃    ┃▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓     ▓▓▓░░░   ┃
┃▓▓ ▓▓▓ ▓ ▓ ▓▓  ▓▓▓   ▓ ▓▓▓  ▓▓  ┃    ┃▓▓       ▓▓▓▓▓▓▓▓▓     ▓▓▓░░░░  ┃
┃ ▓   ▓ ▓ ▓ ▓ ▓ ▓▓ ▓▓▓ ▓    ▓ ▓▓ ┃    ┃               ▓▓▓▓▓▓           ┃
┃ ▓▓  ▓  ▓    ▓  ▓▓▓ ▓▓        ▓▓┃    ┃               ▓▓▓▓▓▓           ┃
┃ ▓ ▓   ▓ ▓ ▓▓  ▓ ▓▓▓▓ ▓▓▓▓▓    ▓┃    ┃          ░░▓▓▓▓▓▓▓▓▓░░▓▓▓▓     ┃
┃    ▓▓▓▓▓ ▓ ▓▓▓▓  ▓ ▓  ▓▓▓▓ ▓   ┃    ┃    ▓▓   ░░░▓▓     ▓▓░░▓▓▓▓▓    ┃
┃   ▓▓▓  ▓ ▓   ▓    ▓▓ ▓   ▓▓▓▓  ┃    ┃    ▓▓                    ▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃   ▓      ▓ ▓   ▓▓ ▓▓▓   ▓▓▓▓ ▓▓┃    ┃                 ▓▓▓▓           ┃
┃▓▓ ▓▓ ▓ ▓▓ ▓  ▓▓ ▓▓▓  ▓    ▓   ▓┃    ┃       ░      ▓▓▓▓▓▓▓         ▓▓┃
┃ ▓  ▓▓ ▓ ▓    ▓▓▓  ▓▓ ▓ ▓▓   ▓▓▓┃    ┃      ░       ▓▓▓▓▓▓▓▓▓▓      ▓▓┃
┃▓     ▓  ▓▓ ▓    ▓▓ ▓▓ ▓ ▓▓▓▓ ▓ ┃    ┃              ▓▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃▓   ▓▓      ▓▓▓ ▓▓ ▓ ▓▓ ▓▓▓  ▓  ┃    ┃              ░▓▓▓▓▓▓▓▓▓▓▓▓     ┃
┃ ▓    ▓  ▓ ▓   ▓ ▓ ▓  ▓▓▓▓▓  ▓  ┃    ┃              ░░▓▓▓▓▓▓▓▓▓▓▓     ┃
┃▓    ▓    ▓ ▓ ▓▓▓  ▓▓▓    ▓ ▓ ▓ ┃    ┃              ░▓▓▓▓▓▓▓▓         ┃
┃    ▓▓     ▓   ▓ ▓ ▓ ▓▓   ▓▓   ▓┃    ┃              ▓▓▓▓▓▓▓▓▓         ┃
┃  ▓▓   ▓▓▓   ▓▓▓  ▓▓  ▓▓  ▓ ▓ ▓ ┃    ┃       ▓▓▓    ▓▓▓▓▓▓▓▓▓         ┃
┃ ▓▓  ▓ ▓ ▓  ▓ ▓ ▓▓▓▓▓▓ ▓  ▓  ▓  ┃    ┃ ▓▓    ▓▓▓    ▓▓▓▓▓▓▓▓▓         ┃
┃ ▓▓    ▓▓▓▓▓  ▓▓ ▓▓  ▓   ▓ ▓▓ ▓ ┃    ┃ ▓▓    ▓▓▓    ▓▓▓▓▓  ▓▓         ┃
┃▓ ▓ ▓▓▓▓   ▓   ▓▓ ▓  ▓▓ ▓   ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓           ▓▓▓        ┃
┃ ▓▓▓▓ ▓  ▓▓ ▓      ▓  ▓▓▓     ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓       ┃
┃▓   ▓  ▓▓▓   ▓     ▓▓▓▓▓  ▓▓    ┃    ┃       ▓▓▓▓▓       ▓▓▓▓▓▓▓      ┃
┃▓ ▓  ▓ ▓ ▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓ ▓▓▓ ┃    ┃        ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓ ▓▓      ▓▓▓▓  ▓▓ ▓▓▓    ▓▓▓▓┃    ┃            ▓▓▓▓  ▓▓▓▓▓▓    ▓▓▓▓┃
┃▓ ▓   ▓▓  ▓  ▓   ▓  ▓ ▓▓   ▓ ▓ ▓┃    ┃                      ▓▓    ░▓▓▓┃
┃▓  ▓▓▓  ▓   ▓   ▓     ▓ ▓ ▓▓   ▓┃    ┃                          ▓▓░░░░┃
┃▓   ▓ ▓   ▓   ▓▓  ▓▓▓▓    ▓▓▓ ▓▓┃    ┃    ▓▓              ▓▓    ▓▓░░░░┃
┃▓   ▓ ▓     ▓▓▓ ▓  ▓ ▓ ▓ ▓▓▓ ▓  ┃    ┃    ▓▓       ▓▓▓▓   ▓▓▓  ▓▓▓░░░ ┃
┃▓▓▓ ▓▓ ▓▓▓  ▓ ▓▓     ▓▓  ▓▓▓  ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓▓▓    ▓▓  ▓▓▓    ┃
┃  ▓▓▓▓  ▓▓   ▓ ▓▓▓▓   ▓  ▓     ▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓  ▓▓  ▓      ┃
┃ ▓ ▓  ▓▓▓   ▓  ▓  ▓▓ ▓ ▓▓▓    ▓ ┃    ┃ ░░    ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓  ▓   ▓ ▓ ▓ ▓▓ ▓▓▓▓ ▓  ▓▓ ▓ ▓┃    ┃ ░░          ▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃ ▓▓           ▓▓▓▓  ▓▓▓ ▓  ▓  ▓ ┃    ┃ ▓▓           ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓       ▓▓ ▓ ▓ ▓ ▓▓▓▓▓ ▓▓▓ ▓  ┃    ┃ ▓▓            ▓▓▓▓▓▓▓▓▓▓░▓▓▓▓▓ ┃
┃▓  ▓ ▓▓▓    ▓  ▓▓ ▓  ▓▓ ▓ ▓ ▓▓▓▓┃    ┃ ▓▓▓▓          ▓▓▓▓  ▓▓▓░░▓▓▓▓▓ ┃
┃ ▓▓ ▓   ▓   ▓   ▓▓▓   ▓ ▓ ▓▓▓▓▓ ┃    ┃ ▓▓▓▓▓          ▓▓▓  ▓▓   ▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓ ▓▓ ▓ ▓   ▓▓▓▓▓   ▓  ▓▓ ┃    ┃ ▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓   ▓▓▓▓▓ ┃
┃  ▓ ▓  ▓▓ ▓ ▓▓ ▓▓▓▓▓▓ ▓  ▓▓ ▓▓▓ ┃    ┃  ▓▓▓▓▓▓         ▓▓▓▓▓    ▓▓▓▓▓ ┃
┃▓ ▓▓▓▓▓ ▓               ▓ ▓▓ ▓  ┃    ┃  ▓▓▓▓▓▓                        ┃
┃   ▓▓▓▓   ▓ ▓ ▓▓▓ ▓     ▓     ▓▓┃    ┃   ▓▓▓▓                         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓      ▓  ▓ ▓ ▓▓▓▓▓▓ ▓▓ ▓  ▓▓▓▓┃    ┃              ▓▓▓▓░▓▓▓▓▓        ┃
┃ ▓▓▓ ▓▓ ▓ ▓  ▓▓▓▓  ▓ ▓▓▓  ▓▓    ┃    ┃  ▓▓          ▓▓▓▓▓▓▓▓▓▓  ▓▓    ┃
┃▓  ▓   ▓ ▓ ▓▓  ▓▓ ▓  ▓    ▓▓ ▓  ┃    ┃ ▓▓▓          ▓▓▓▓▓▓▓▓▓   ▓▓    ┃
┃▓ ▓▓  ▓▓   ▓  ▓▓ ▓▓▓▓ ▓▓▓  ▓ ▓ ▓┃    ┃▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓▓▓▓    ▓▓    ┃
┃▓▓▓▓▓   ▓▓▓▓ ▓▓▓▓ ▓ ▓    ▓▓▓  ▓ ┃    ┃▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓  ┃
┃  ▓ ▓ ▓▓▓ ▓ ▓▓ ▓ ▓▓▓    ▓▓▓ ▓▓▓ ┃    ┃▓▓▓▓░░░▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓ ▓ ▓▓▓▓ ▓ ▓▓ ▓ ▓▓▓  ▓▓▓ ┃    ┃ ▓▓▓░░░▓▓▓▓▓▓▓▓▓▓▓▓▓░░░▓▓▓  ▓▓▓ ┃
┃▓  ▓  ▓▓▓▓ ▓ ▓   ▓▓ ▓ ▓▓▓    ▓  ┃    ┃ ▓▓▓░░░▓▓▓▓▓▓     ▓▓░░░▓▓▓  ▓▓  ┃
┃ ▓▓  ▓ ▓  ▓▓▓     ▓▓▓  ▓ ▓  ▓▓  ┃    ┃   ░░░     ▓▓     ▓▓░░░▓▓▓  ▓▓  ┃
┃   ▓▓ ▓▓    ▓ ▓▓▓    ▓▓ ▓▓ ▓ ▓▓▓┃    ┃   ▓▓▓        ▓▓▓      ▓▓▓░░▓▓▓ ┃
┃▓▓ ▓▓▓  ▓▓  ▓ ▓▓▓ ▓    ▓▓ ▓ ▓▓▓ ┃    ┃   ▓▓▓        ▓▓▓      ▓▓▓░░▓▓▓ ┃
┃   ▓ ▓     ▓       ▓▓   ▓▓   ▓▓▓┃    ┃   ▓▓                  ▓▓    ▓▓ ┃
┃ ▓▓▓▓  ▓▓▓▓   ▓▓ ▓▓ ▓ ▓▓    ▓▓▓ ┃    ┃  ▓▓   ▓▓▓▓     ▓▓▓▓   ▓▓    ▓▓ ┃
┃▓  ▓   ▓▓ ▓▓    ▓▓▓▓   ▓▓▓▓  ▓▓▓┃    ┃  ▓▓   ▓▓▓▓     ▓▓▓▓   ▓▓▓▓  ▓▓ ┃
┃  ▓▓     ▓▓   ▓ ▓▓▓▓  ▓ ▓ ▓▓ ▓▓ ┃    ┃  ▓▓            ▓▓▓▓   ▓▓▓▓  ▓▓ ┃
┃▓▓ ▓▓ ▓▓   ▓▓  ▓  ▓▓▓▓  ▓  ▓  ▓▓┃    ┃  ▓▓▓     ░      ▓▓▓▓▓          ┃
┃    ▓    ▓▓ ▓▓▓  ▓  ▓▓ ▓  ▓   ▓ ┃    ┃  ▓▓▓     ░▓▓▓▓  ▓▓▓▓▓          ┃
┃  ▓▓▓ ▓▓▓▓ ▓ ▓▓ ▓ ▓▓  ▓▓ ▓▓▓▓  ▓┃    ┃  ▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓▓▓▓ ▓▓▓   ┃
┃ ▓▓ ▓   ▓   ▓ ▓  ▓  ▓▓ ▓▓  ▓▓▓  ┃    ┃  ▓▓▓  ▓▓▓▓  ▓▓▓     ▓▓▓▓ ▓▓▓   ┃
┃▓  ▓ ▓ ▓▓▓▓   ▓▓▓     ▓▓▓ ▓  ▓ ▓┃    ┃     ▓▓▓▓▓▓  ▓▓▓▓    ▓▓▓▓ ▓▓▓   ┃
┃ ▓ ▓ ▓▓▓▓ ▓▓▓▓▓ ▓ ▓▓▓▓  ▓ ▓▓▓   ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ┃
┃  ▓  ▓▓  ▓ ▓▓▓ ▓▓▓ ▓▓▓ ▓▓   ▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓┃
┃ ▓▓▓  ▓▓▓ ▓   ▓ ▓▓▓  ▓  ▓ ▓ ▓ ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓   ░░░░    ▓▓▓┃
┃ ▓   ▓▓▓▓▓▓ ▓▓       ▓ ▓ ▓▓  ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓      ░░░░    ▓▓ ┃
┃▓   ▓ ▓  ▓ ▓▓▓▓  ▓  ▓ ▓▓  ▓▓ ▓  ┃    ┃     ▓▓▓   ▓▓▓▓      ▓▓▓▓       ┃
┃  ▓▓▓ ▓▓     ▓▓  ▓▓  ▓▓  ▓    ▓ ┃    ┃   ▓▓▓▓      ▓▓      ▓▓▓▓▓▓     ┃
┃▓  ▓ ▓  ▓ ▓▓   ▓ ▓   ▓▓▓▓▓▓   ▓ ┃    ┃   ▓▓▓   ▓▓          ▓▓▓▓▓▓     ┃
┃▓  ▓▓▓   ▓▓ ▓ ▓   ▓ ▓   ▓ ▓▓ ▓▓ ┃    ┃   ▓▓▓   ▓▓▓            ▓▓▓  ▓▓ ┃
┃ ▓▓  ▓▓  ▓▓▓▓  ▓▓   ▓▓  ▓   ▓ ▓▓┃    ┃  ▓▓▓▓▓  ▓▓▓▓▓▓▓             ▓▓ ┃
┃▓ ▓▓ ▓▓ ▓ ▓▓▓▓▓▓ ▓ ▓▓ ▓▓▓▓   ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓         ▓▓ ┃
┃  ▓ ▓ ▓▓▓▓▓▓▓ ▓▓▓▓▓▓      ▓  ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓            ┃
┃▓▓ ▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓▓  ▓ ▓  ▓ ▓  ▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓             ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓  ▓▓▓▓ ▓ ▓ ▓▓▓    ▓ ▓▓▓ ▓▓▓▓┃    ┃       ▓▓▓     ▓▓▓      ▓▓▓░    ┃
┃  ▓▓ ▓ ▓▓▓ ▓▓▓▓ ▓▓▓▓   ▓▓▓▓▓   ▓┃    ┃  ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓░    ┃
┃▓ ▓  ▓▓  ▓▓▓ ▓   ▓▓  ▓▓   ▓ ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ░    ┃
┃▓▓▓▓▓ ▓ ▓▓  ▓ ▓▓▓▓▓ ▓   ▓▓ ▓▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓             ┃
┃▓▓▓▓▓ ▓▓▓    ▓▓   ▓ ▓▓    ▓    ▓┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓          ┃
┃ ▓  ▓▓▓   ▓▓▓▓▓▓ ▓▓▓ ▓▓▓ ▓▓ ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓   ┃
┃  ▓▓▓ ▓ ▓ ▓▓▓▓▓▓▓  ▓▓▓ ▓   ▓▓   ┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓   ┃
┃▓▓▓▓  ▓▓▓ ▓ ▓▓   ▓▓▓ ▓▓▓    ▓ ▓▓┃    ┃ ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓   ┃
┃ ▓ ▓ ▓▓▓ ▓▓▓ ▓▓▓▓▓  ▓ ▓▓▓▓▓▓▓   ┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓▓ ▓  ▓▓ ▓▓▓▓▓ ▓ ▓▓▓ ▓ ▓▓  ▓▓ ▓ ┃    ┃▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓   ▓  ▓▓   ▓▓▓ ▓      ▓▓▓  ▓▓  ┃    ┃▓▓         ▓▓▓▓▓▓▓▓▓   ▓▓▓      ┃
┃▓▓     ▓   ▓    ▓▓▓▓    ▓ ▓ ▓  ▓┃    ┃           ▓▓   ▓▓▓▓   ▓▓▓      ┃
┃  ▓▓    ▓▓  ▓   ▓  ▓▓  ▓▓▓▓  ▓▓▓┃    ┃        ▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓   ▓▓▓┃
┃▓▓   ▓  ▓▓▓▓ ▓ ▓▓ ▓▓▓  ▓   ▓ ▓▓ ┃    ┃        ▓▓▓▓▓   ▓▓▓▓▓       ▓▓▓▓┃
┃  ▓ ▓▓▓▓ ▓▓ ▓▓   ▓▓ ▓      ▓▓▓▓▓┃    ┃     ▓▓ ▓▓▓▓▓▓   ▓▓▓▓      ▓▓▓▓▓┃
┃▓ ▓ ▓ ▓    ▓▓ ▓ ▓   ▓▓    ▓▓▓▓▓▓┃    ┃     ▓▓  ▓▓▓▓▓      ▓▓     ▓▓▓▓▓┃
┃▓ ▓  ▓▓ ▓ ▓▓▓ ▓ ▓  ▓ ▓  ▓▓ ▓    ┃    ┃▓▓▓  ▓▓  ▓▓▓▓▓▓     ▓▓   ▓▓▓▓   ┃
┃▓▓▓  ▓▓ ▓▓ ▓▓▓▓   ▓▓ ▓▓  ▓▓ ▓▓▓ ┃    ┃▓▓▓  ▓▓▓▓▓▓▓▓▓▓     ▓▓   ▓▓▓    ┃
┃   ▓▓▓▓▓▓▓ ▓▓ ▓▓   ▓ ▓   ▓▓  ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓  ▓▓     ┃
┃ ▓▓▓▓ ▓▓▓▓ ▓   ▓ ▓ ▓▓▓▓ ▓  ▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓        ┃
┃▓ ▓    ▓ ▓ ▓     ▓▓  ▓▓▓        ┃    ┃  ▓▓   ▓▓▓▓▓     ▓▓  ▓▓▓▓       ┃
┃ ▓▓▓   ▓  ▓▓  ▓▓ ▓▓  ▓▓▓▓▓ ▓  ▓ ┃    ┃  ▓▓      ▓▓     ▓▓  ▓▓▓▓       ┃
┃▓ ▓▓ ▓   ▓ ▓   ▓ ▓ ▓  ▓▓▓ ▓     ┃    ┃ ▓▓▓▓     ▓▓      ▓   ▓▓▓       ┃
┃  ▓ ▓▓▓    ▓   ▓  ▓▓    ▓ ▓ ▓▓ ▓┃    ┃ ▓▓▓▓▓▓   ▓▓      ▓▓        ▓▓  ┃
┃ ▓▓ ▓▓▓   ▓▓      ▓▓ ▓▓   ▓ ▓▓  ┃    ┃ ▓▓▓▓▓▓   ▓▓      ▓▓        ▓▓  ┃
┃ ▓▓▓ ▓    ▓▓▓▓▓▓   ▓  ▓▓▓  ▓▓▓  ┃    ┃ ▓▓▓▓▓▓   ▓▓▓▓▓▓  ▓▓        ▓▓  ┃
┃ ▓   ▓▓▓ ▓ ▓▓▓ ▓▓▓▓   ▓  ▓  ▓▓  ┃    ┃ ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓  ┃
┃▓▓▓▓  ▓▓▓▓   ▓▓ ▓▓▓▓▓   ▓▓      ┃    ┃ ▓▓   ▓▓▓  ▓▓▓▓▓▓▓▓▓            ┃
┃          ▓ ▓ ▓ ▓   ▓ ▓  ▓▓   ▓▓┃    ┃               ░░░░░          ▓▓┃
┃ ▓   ▓    ▓▓   ▓  ▓▓  ▓  ▓ ▓▓▓▓▓┃    ┃                ░░░░        ▓▓▓▓┃
┃ ▓▓  ▓▓▓▓▓    ▓ ▓ ▓ ▓▓▓▓  ▓ ▓▓▓ ┃    ┃     ▓▓          ░░░       ░▓▓▓▓┃
┃▓  ▓ ▓▓   ▓▓▓ ▓▓ ▓ ▓   ▓▓▓ ▓  ▓▓┃    ┃     ▓▓                         ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓ ▓  ▓▓▓▓▓  ▓▓   ▓ ▓▓    ▓▓  ▓▓┃    ┃                   ▓▓▓    ▓▓    ┃
┃ ▓ ▓      ▓ ▓  ▓▓ ▓▓▓▓   ▓▓▓ ▓▓ ┃    ┃  ▓▓           ▓▓▓▓▓▓▓    ▓▓    ┃
┃▓ ▓▓ ▓  ▓    ▓ ▓▓▓  ▓     ▓     ┃    ┃  ▓▓          ▓▓▓  ░░           ┃
┃  ▓ ▓▓ ▓   ▓▓  ▓▓  ▓  ▓ ▓ ▓   ▓▓┃    ┃  ▓▓       ▓▓▓▓▓▓  ░░         ▓▓┃
┃  ▓▓ ▓     ▓▓▓▓▓    ▓▓▓ ▓▓  ▓ ▓▓┃    ┃  ▓▓       ▓▓▓▓▓   ▓▓▓       ▓▓▓┃
┃▓ ▓      ▓▓▓▓  ▓  ▓▓▓ ▓   ▓▓▓▓▓▓┃    ┃  ▓▓      ▓▓▓▓    ▓▓▓▓   ▓▓▓▓▓▓▓┃
┃  ▓▓ ▓▓    ▓▓▓  ▓ ▓▓ ▓  ▓ ▓ ▓ ▓▓┃    ┃  ▓▓      ▓▓▓▓   ▓▓▓▓▓   ▓▓▓▓▓▓▓┃
┃  ▓▓    ▓▓▓▓▓▓▓ ▓▓ ▓▓▓  ▓▓▓▓▓▓▓▓┃    ┃  ▓▓    ▓▓▓▓▓▓   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓┃
┃▓  ▓ ▓▓▓▓     ▓  ▓  ▓▓▓▓    ▓ ▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓  ▓▓▓ ▓▓ ▓▓  ▓  ▓▓▓▓ ▓▓▓▓▓▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃   ▓ ▓▓▓ ▓▓ ▓  ▓      ▓ ▓ ▓▓  ▓▓┃    ┃   ▓▓▓▓▓▓▓▓          ▓▓▓▓▓▓▓▓▓  ┃
┃▓  ▓▓▓▓▓▓▓▓    ▓    ▓ ▓ ▓  ▓▓   ┃    ┃   ▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓  ┃
┃▓▓ ▓▓ ▓▓  ▓  ▓▓▓ ▓ ▓ ▓▓ ▓▓▓▓ ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓   ▓▓▓       ▓▓▓▓▓▓▓ ┃
┃ ▓▓ ▓   ▓▓ ▓▓  ▓▓ ▓▓    ▓▓ ▓▓▓▓▓┃    ┃ ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓ ┃
┃ ▓   ▓▓▓  ▓ ▓ ▓   ▓▓  ▓▓     ▓  ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓            ┃
┃ ▓ ▓ ▓▓ ▓▓ ▓▓▓ ▓▓   ▓   ▓ ▓   ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓  ▓            ┃
┃▓   ▓▓ ▓▓▓ ▓  ▓▓▓▓ ▓▓▓▓ ▓ ▓▓ ▓  ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓░░▓▓    ┃
┃▓▓ ▓    ▓▓ ▓▓▓▓  ▓ ▓ ▓▓▓ ▓▓▓▓  ▓┃    ┃▓▓▓▓    ▓▓▓▓▓▓▓▓   ▓▓▓▓▓░░▓▓    ┃
┃▓▓▓▓  ▓    ▓    ▓  ▓  ▓▓▓  ▓  ▓ ┃    ┃▓▓▓▓       ▓▓▓        ▓▓░░░░    ┃
┃▓ ▓ ▓▓▓   ▓▓▓▓    ▓ ▓    ▓ ▓    ┃    ┃ ▓▓▓▓      ▓▓▓         ░░░░░    ┃
┃  ▓▓   ▓ ▓  ▓▓   ▓ ▓▓ ▓ ▓ ▓ ▓▓▓▓┃    ┃  ▓▓▓▓▓▓   ▓▓▓    ▓▓   ░░▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓▓▓▓ ▓  ▓   ▓ ▓  ▓▓▓▓▓▓  ▓▓┃    ┃  ▓▓▓▓▓▓    ▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓  ▓▓   ▓ ▓ ▓▓  ▓▓ ▓   ▓▓ ▓▓ ▓┃    ┃  ▓  ▓▓▓     ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓▓ ▓▓▓ ▓  ▓▓▓ ▓   ▓▓▓▓  ▓▓▓▓▓▓┃    ┃▓▓▓  ▓▓▓▓    ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓▓▓  ▓▓ ▓▓▓     ▓ ▓  ▓▓▓▓  ▓  ▓▓┃    ┃▓▓▓▓ ▓▓▓▓▓▓         ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓▓  ▓▓▓▓    ▓▓  ▓▓▓▓ ▓▓▓ ▓▓ ▓┃    ┃ ▓▓▓  ▓▓▓▓▓    ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓    ▓▓▓▓▓▓   ▓▓    ▓   ▓  ▓ ▓▓┃    ┃      ▓▓▓▓▓    ▓▓           ▓▓▓▓┃
┃   ▓ ▓▓▓▓  ▓  ▓▓▓   ▓  ▓   ▓ ▓▓▓┃    ┃      ▓▓▓      ▓▓           ▓▓▓▓┃
┃▓ ▓   ▓▓    ▓▓   ▓ ▓▓   ▓  ▓▓ ▓ ┃    ┃      ▓▓▓      ▓▓▓▓▓▓      ▓▓▓▓▓┃
┃▓ ▓ ▓▓  ▓ ▓  ▓ ▓▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓▓┃    ┃      ▓▓▓      ▓▓▓▓▓▓  ▓▓  ▓▓▓▓ ┃
┃    ▓ ▓▓ ▓▓   ▓  ▓ ▓▓  ▓▓ ▓ ▓▓▓ ┃    ┃                  ▓▓▓▓▓▓▓   ▓▓▓ ┃
┃ ▓ ▓▓▓    ▓▓ ▓ ▓    ▓▓▓▓     ▓▓ ┃    ┃                    ▓▓▓▓     ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃   ▓     ▓▓  ▓  ▓ ▓ ▓▓ ▓  ▓ ▓▓▓ ┃    ┃                    ▓▓       ▓▓ ┃
┃▓▓▓ ▓▓  ▓▓  ▓▓      ▓▓  ▓▓▓  ▓▓ ┃    ┃▓▓▓▓▓▓   ▓▓         ▓▓     ▓▓▓▓ ┃
┃▓▓▓ ▓▓   ▓▓  ▓   ▓ ▓ ▓ ▓ ▓  ▓▓▓ ┃    ┃▓▓▓▓▓▓   ▓▓        ▓▓▓    ▓▓▓▓▓ ┃
┃▓▓▓ ▓ ▓ ▓ ▓▓ ▓▓▓ ▓▓▓▓▓ ▓▓ ▓ ▓ ▓▓┃    ┃▓▓▓▓▓▓░░░▓▓  ▓▓   ▓▓▓▓   ░▓▓▓▓▓▓┃
┃▓ ▓ ▓▓ ▓ ▓   ▓▓ ▓  ▓▓   ▓ ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓░░░░▓  ▓▓   ▓▓▓     ▓▓▓▓▓▓┃
┃  ▓ ▓ ▓ ▓ ▓ ▓▓▓ ▓ ▓    ▓  ▓▓ ▓ ▓┃    ┃  ▓▓▓▓░░░░▓▓▓▓▓   ▓▓▓     ▓▓▓▓  ┃
┃  ▓▓▓▓▓▓ ▓▓ ▓     ▓▓▓▓▓     ▓   ┃    ┃  ▓▓▓▓░░░░▓▓▓▓▓   ▓▓▓           ┃
┃  ▓  ▓  ▓ ▓▓▓▓▓▓▓  ▓    ▓▓▓    ▓┃    ┃  ▓▓▓▓    ▓▓▓▓▓   ▓▓▓           ┃
┃▓ ▓ ▓▓  ▓  ▓ ▓ ▓ ▓ ▓▓ ▓▓▓    ▓  ┃    ┃  ▓▓▓▓     ▓▓▓▓▓▓     ▓▓▓       ┃
┃  ▓ ▓ ▓   ▓ ▓▓▓  ▓▓   ▓▓     ▓  ┃    ┃  ░░░      ▓▓▓▓▓▓     ▓▓▓       ┃
┃▓  ▓ ▓▓     ▓ ▓▓▓     ▓▓▓▓▓    ▓┃    ┃  ░░░      ▓▓▓▓▓▓     ▓▓▓▓      ┃
┃ ▓▓▓▓  ▓  ▓▓▓▓ ▓▓ ▓   ▓▓▓▓   ▓  ┃    ┃  ▓▓▓      ▓▓▓▓▓▓     ▓▓▓▓▓     ┃
┃▓   ▓   ▓ ▓ ▓ ▓ ▓  ▓  ▓▓ ▓▓▓▓▓▓▓┃    ┃  ▓▓▓      ▓▓▓▓▓▓     ▓▓▓▓▓▓▓   ┃
┃ ▓▓▓ ▓  ▓▓   ▓▓ ▓  ▓ ▓▓▓ ▓  ▓  ▓┃    ┃ ▓▓▓▓   ▓▓▓░▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓   ┃
┃▓  ▓▓▓ ▓▓▓▓ ▓ ▓ ▓▓▓▓▓▓▓▓  ▓▓▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ▓▓▓   ┃
┃▓ ▓ ▓▓▓ ▓▓     ▓▓ ▓ ▓ ▓▓  ▓ ▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓┃
┃▓▓▓   ▓▓ ▓▓▓▓▓  ▓▓ ▓  ▓  ▓    ▓▓┃    ┃▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓░     ▓▓▓▓┃
┃ ▓ ▓  ▓▓▓  ▓▓▓▓▓▓▓ ▓ ▓ ▓   ▓ ▓  ┃    ┃ ▓▓   ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓ ┃
┃ ▓▓ ▓ ▓   ▓ ▓▓▓▓  ▓ ▓▓▓  ▓▓ ▓▓▓ ┃    ┃ ▓▓▓      ▓▓▓▓▓▓  ▓▓▓▓▓    ▓▓▓▓ ┃
┃▓▓▓▓▓▓   ▓  ▓▓▓   ▓▓▓▓▓ ▓  ▓▓ ▓ ┃    ┃▓▓▓▓       ▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓▓ ┃
┃▓▓        ▓    ▓▓▓      ▓▓▓▓  ▓▓┃    ┃▓▓             ▓▓▓▓▓    ▓▓▓▓  ▓▓┃
┃    ▓▓▓▓▓ ▓ ▓  ▓ ▓▓▓▓  ▓ ▓▓   ▓▓┃    ┃       ▓▓▓▓    ▓▓▓▓▓    ▓▓▓   ▓▓┃
┃  ▓  ▓  ▓▓ ▓▓ ▓ ▓▓▓ ▓ ▓▓  ▓ ▓▓▓▓┃    ┃       ▓▓▓▓▓   ▓▓▓▓▓         ▓▓▓┃
┃▓ ▓▓   ▓ ▓▓ ▓   ▓     ▓ ▓ ▓  ▓ ▓┃    ┃       ▓▓▓▓▓▓  ▓▓▓          ▓▓▓▓┃
┃   ▓▓ ▓▓▓ ▓▓ ▓▓▓▓▓ ▓▓▓     ▓▓▓▓▓┃    ┃   ▓▓  ▓▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓┃
┃▓▓  ▓  ▓   ▓ ▓▓ ▓▓  ▓  ▓▓▓   ▓▓▓┃    ┃   ▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓┃
┃▓ ▓ ▓▓ ▓▓ ▓ ▓  ▓ ▓▓▓▓  ▓ ▓  ▓ ▓ ┃    ┃   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓ ┃
┃ ▓▓▓  ▓   ▓ ▓▓▓▓▓   ▓ ▓▓▓    ▓▓ ┃    ┃     ▓▓▓  ▓▓▓▓▓▓▓      ░     ▓▓ ┃
┃▓    ▓▓▓▓▓▓  ▓▓  ▓  ▓▓    ▓  ▓ ▓┃    ┃ ░   ▓▓▓▓░   ▓▓▓      ░░     ░░ ┃
┃▓▓▓ ▓▓  ▓ ▓   ▓▓ ▓  ▓ ▓▓ ▓    ▓ ┃    ┃▓▓  ▓▓       ▓▓▓       ▓▓    ░░ ┃
┃▓ ▓ ▓▓   ▓ ▓ ▓▓▓       ▓▓▓   ▓▓ ┃    ┃▓▓  ▓▓       ▓▓▓       ▓▓    ▓▓ ┃
┃▓    ▓    ▓▓ ▓   ▓▓ ▓▓▓  ▓▓  ▓▓ ┃    ┃                             ▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓ ▓▓   ▓ ▓  ▓▓▓▓ ▓▓▓▓  ▓ ▓▓▓  ┃    ┃              ▓▓▓▓▓▓▓       ▓▓  ┃
┃▓  ▓     ▓ ▓ ▓▓  ▓▓▓    ▓▓ ▓ ▓▓ ┃    ┃              ▓▓▓▓▓▓▓       ▓▓  ┃
┃▓  ▓ ▓ ▓▓▓  ▓  ▓▓▓▓ ▓     ▓ ▓  ▓┃    ┃       ▓▓▓▓▓   ▓▓▓▓▓▓       ▓▓  ┃
┃   ▓   ▓ ▓▓▓▓  ▓▓▓  ▓▓▓▓ ▓▓▓▓▓  ┃    ┃       ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓  ┃
┃▓▓ ▓▓▓ ▓▓▓▓▓ ▓ ▓▓▓▓▓▓▓ ▓     ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓ ┃
┃  ▓   ▓▓▓▓   ▓▓▓▓  ▓▓▓▓  ▓ ▓ ▓▓ ┃    ┃     ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓     ▓▓ ┃
┃▓    ▓▓ ▓  ▓    ▓ ▓   ▓▓▓ ▓▓ ▓  ┃    ┃     ▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓  ▓  ▓▓▓▓  ▓▓▓▓ ▓▓ ▓▓▓ ▓ ▓▓▓▓┃    ┃     ▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓▓▓▓ ▓▓ ▓ ▓▓  ▓▓ ▓ ▓ ▓ ▓▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓   ▓┃
┃  ▓▓ ▓▓ ▓▓▓▓      ▓▓▓▓▓ ▓▓ ▓   ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓   ▓┃
┃▓▓  ▓▓ ▓ ▓  ▓▓▓ ▓ ▓▓▓▓ ▓▓▓ ▓ ▓ ▓┃    ┃   ▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓▓▓▓▓▓▓  ▓▓┃
┃   ▓▓▓ ▓▓  ▓  ▓ ▓ ▓▓▓▓▓  ▓ ▓ ▓▓▓┃    ┃   ▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓      ▓▓▓┃
┃   ▓▓ ▓ ▓▓  ▓▓  ▓ ▓▓ ▓▓▓  ▓ ▓ ▓▓┃    ┃   ▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓      ▓▓▓┃
┃▓▓▓  ▓▓ ▓▓  ▓▓▓▓ ▓   ▓     ▓▓▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓               ┃
┃▓▓▓▓  ▓▓▓  ▓▓▓▓   ▓▓   ▓        ┃    ┃▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓              ┃
┃▓▓▓▓ ▓▓▓▓   ▓▓  ▓▓  ▓ ▓▓    ▓   ┃    ┃▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓              ┃
┃▓ ▓  ▓▓   ▓▓ ▓▓▓▓ ▓  ▓▓         ┃    ┃▓▓   ▓▓    ▓▓▓▓▓▓▓    ▓▓        ┃
┃▓   ▓      ▓     ▓    ▓ ▓   ▓  ▓┃    ┃▓▓              ▓▓    ▓▓        ┃
┃▓▓ ▓ ▓  ▓▓     ▓▓▓ ▓ ▓▓▓▓▓ ▓▓▓▓▓┃    ┃▓▓▓▓            ▓▓    ▓▓▓▓▓▓▓▓  ┃
┃ ▓▓▓    ▓ ▓▓ ▓▓ ▓ ▓       ▓▓▓  ▓┃    ┃ ▓▓▓       ▓▓▓▓▓▓▓▓      ▓▓▓▓▓  ┃
┃ ▓▓▓ ▓  ▓  ▓▓▓▓▓▓ ▓▓ ▓▓▓▓▓ ▓▓ ▓ ┃    ┃ ▓▓▓       ▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓   ┃
┃       ▓▓▓ ▓▓ ▓ ▓ ▓▓▓    ▓▓▓▓  ▓┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓   ┃
┃▓▓  ▓▓  ▓ ▓▓ ▓▓▓ ▓ ▓▓ ▓▓   ▓▓▓  ┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓   ┃
┃ ▓ ▓ ▓▓ ▓ ▓ ▓ ▓▓ ▓▓ ▓▓▓  ▓▓   ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓ ▓  ▓▓▓▓  ▓  ▓▓ ▓  ▓▓▓ ▓▓▓▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃   ▓▓▓▓▓  ▓▓▓ ▓▓ ▓▓▓▓  ▓▓▓▓▓  ▓▓┃    ┃    ▓▓▓▓▓▓▓▓░▓▓▓▓▓▓▓▓  ▓▓▓▓▓    ┃
┃ ▓   ▓ ▓ ▓ ▓  ▓   ▓▓▓  ▓  ▓▓   ▓┃    ┃     ▓▓▓▓▓▓░░    ▓▓▓▓    ▓▓▓    ┃
┃▓ ▓  ▓ ▓ ▓▓ ▓▓   ▓▓▓    ▓ ▓▓▓   ┃    ┃     ▓▓▓▓▓░░░    ▓▓▓▓     ▓▓    ┃
┃ ▓▓▓▓▓ ▓▓▓ ▓▓ ▓▓▓   ▓ ▓  ▓▓▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓░░▓▓▓▓▓▓        ▓▓    ┃
┃▓▓ ▓      ▓ ▓  ▓▓▓▓ ▓ ▓▓   ▓ ▓ ▓┃    ┃ ▓▓▓▓▓      ▓▓▓▓▓▓    ▓▓        ┃
┃ ▓  ▓▓▓▓▓   ▓▓  ▓▓   ▓ ▓▓ ▓ ▓   ┃    ┃ ▓▓▓▓  ▓▓   ▓▓▓▓▓▓    ▓▓        ┃
┃ ▓▓▓  ▓ ▓▓  ▓▓▓▓ ▓  ▓▓ ▓   ▓ ▓ ▓┃    ┃       ▓▓   ▓▓▓                 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓  ▓  ▓▓ ▓▓ ▓   ▓▓▓▓ ▓▓ ▓▓ ▓┃    ┃   ▓▓       ▓▓▓             ▓▓  ┃
┃ ▓  ▓▓ ▓    ▓▓▓  ▓▓ ▓  ▓▓ ▓ ▓▓ ▓┃    ┃  ▓▓▓       ▓▓▓  ▓▓         ▓▓  ┃
┃▓▓▓▓▓    ▓ ▓▓ ▓▓ ▓▓ ▓  ▓     ▓ ▓┃    ┃▓▓▓▓▓       ▓▓▓  ▓▓░        ░░  ┃
┃▓▓▓  ▓▓       ▓    ▓ ▓    ▓▓ ▓  ┃    ┃▓▓▓               ░         ░░  ┃
┃▓ ▓   ▓ ▓   ▓▓    ▓  ▓ ▓▓  ▓ ▓  ┃    ┃▓▓▓  ▓▓▓                    ░░  ┃
┃▓ ▓▓▓▓▓▓▓ ▓▓▓ ▓▓▓  ▓ ▓▓ ▓▓  ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓  ░░  ┃
┃  ▓▓ ▓▓  ▓▓▓▓ ▓▓▓▓▓▓   ▓ ▓▓ ▓▓  ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓  ▓▓  ┃
┃ ▓    ▓ ▓▓    ▓     ▓   ▓    ▓▓▓┃    ┃      ▓▓▓    ▓▓▓            ▓▓▓ ┃
┃ ▓    ▓▓   ▓▓▓▓▓           ▓▓  ▓┃    ┃      ▓▓     ▓▓▓            ▓▓▓ ┃
┃▓ ▓▓ ▓ ▓    ▓ ▓  ▓▓ ▓▓ ▓▓▓ ▓ ▓▓ ┃    ┃ ▓▓          ▓▓▓     ▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓      ▓     ▓▓  ▓ ▓▓  ▓▓  ▓▓▓┃    ┃ ▓▓▓         ▓▓▓     ▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓▓▓ ▓▓▓▓▓▓▓  ▓ ▓  ▓  ▓▓  ▓ ┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓▓▓▓▓▓    ▓▓   ▓▓▓ ▓▓ ▓▓▓▓ ▓▓ ┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓  ▓▓▓ ▓▓    ▓▓  ▓▓▓ ▓  ▓▓▓ ┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓     ▓▓▓▓▓▓ ▓▓  ▓ ▓▓▓▓▓▓ ▓ ▓▓ ▓┃    ┃▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓      ▓▓▓▓▓ ▓▓▓▓ ▓   ▓▓▓▓▓▓▓┃    ┃▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓┃
┃ ▓ ▓ ▓  ▓▓ ▓▓▓ ▓ ▓▓    ▓ ▓▓▓ ▓▓▓┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓┃
┃▓     ▓ ▓    ▓▓▓    ▓▓▓  ▓ ▓▓▓ ▓┃    ┃        ▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓ ┃
┃  ▓  ▓ ▓ ▓ ▓▓  ▓ ▓ ▓▓     ▓▓▓   ┃    ┃       ▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓   ┃
┃ ▓ ▓ ▓   ▓▓▓▓▓ ▓▓▓ ▓▓    ▓▓▓  ▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓    ┃
┃  ▓▓▓ ▓▓▓▓  ▓▓     ▓ ▓ ▓▓▓▓  ▓ ▓┃    ┃      ▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓    ┃
┃      ▓▓▓ ▓   ▓  ▓ ▓ ▓▓▓   ▓ ▓ ▓┃    ┃      ▓▓▓▓▓        ▓▓▓▓▓  ▓▓    ┃
┃    ▓   ▓▓ ▓  ▓ ▓▓▓ ▓     ▓▓ ▓ ▓┃    ┃       ▓▓▓▓   ▓▓   ▓      ▓▓▓▓▓ ┃
┃     ▓ ▓▓▓▓▓▓ ▓▓  ▓  ▓▓  ▓▓▓▓▓ ▓┃    ┃        ▓▓▓ ▓▓▓▓  ▓▓     ▓▓▓▓▓▓ ┃
┃ ▓ ▓     ▓ ▓ ▓▓▓  ▓▓     ▓▓▓ ▓▓ ┃    ┃            ▓▓▓▓  ▓▓     ▓▓▓▓▓▓ ┃
┃ ▓▓ ▓  ▓     ▓  ▓▓▓▓ ▓▓   ▓▓  ▓ ┃    ┃ ▓▓         ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓    ┃
┃▓ ▓▓  ▓▓    ▓▓ ▓▓▓▓ ▓▓▓  ▓▓ ▓ ▓ ┃    ┃ ▓▓   ▓▓    ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓    ┃
┃ ▓  ▓▓▓  ▓▓ ▓▓ ▓▓ ▓ ▓▓   ▓ ▓    ┃    ┃ ▓    ▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓   ▓▓     ┃
┃▓▓ ▓ ▓ ▓ ▓ ▓     ▓  ▓  ▓▓    ▓ ▓┃    ┃▓▓    ▓▓▓▓▓         ▓▓  ▓▓▓     ┃
┃▓▓    ▓ ▓▓▓▓   ▓  ▓ ▓▓▓ ▓▓▓ ▓  ▓┃    ┃▓▓     ▓▓▓▓         ▓▓  ▓▓▓     ┃
┃▓   ▓ ▓▓▓  ▓ ▓ ▓▓▓      ▓ ▓  ▓ ▓┃    ┃       ▓▓▓     ▓▓▓      ▓▓▓     ┃
┃ ▓ ▓    ▓▓  ▓▓▓ ▓▓ ▓  ▓ ▓ ▓▓ ▓  ┃    ┃               ▓▓▓              ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓ ▓  ▓ ▓ ▓   ▓▓▓▓▓    ▓▓▓▓▓ ▓┃    ┃   ▓▓           ▓▓▓      ▓▓     ┃
┃▓  ▓▓   ▓▓ ▓  ▓ ▓▓ ▓     ▓    ▓ ┃    ┃   ▓▓▓          ▓▓▓▓     ▓▓     ┃
┃ ▓ ▓▓▓▓   ▓  ▓ ▓  ▓ ▓▓▓▓▓▓▓▓   ▓┃    ┃  ▓▓▓▓             ▓▓▓▓▓▓▓▓     ┃
┃  ▓▓   ▓ ▓▓▓  ▓ ▓  ▓▓  ▓▓ ▓  ▓  ┃    ┃  ▓▓▓▓   ▓▓▓       ▓▓▓▓▓▓▓      ┃
┃▓ ▓▓▓ ▓  ▓ ▓▓ ▓ ▓▓ ▓  ▓▓▓▓   ▓  ┃    ┃  ▓▓▓▓   ▓▓▓       ▓▓▓▓▓▓       ┃
┃▓  ▓▓▓   ▓▓▓ ▓    ▓▓▓▓▓▓   ▓  ▓▓┃    ┃  ▓▓▓▓   ▓▓▓▓      ▓▓▓▓▓      ▓▓┃
┃▓▓ ▓▓ ▓▓    ▓ ▓ ▓   ▓ ▓▓   ▓  ▓▓┃    ┃▓▓▓▓▓▓▓   ▓▓▓▓      ▓▓▓▓      ▓▓┃
┃ ▓▓▓▓  ▓  ▓▓ ▓▓     ▓▓  ▓ ▓  ▓▓ ┃    ┃▓▓▓▓▓▓▓▓  ▓▓▓▓▓              ▓▓▓┃
┃▓▓ ▓▓▓▓▓▓▓▓▓ ▓▓  ▓▓    ▓ ▓▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓          ▓▓ ┃
┃ ▓ ▓▓  ▓  ▓  ▓▓  ▓▓▓▓▓▓▓   ▓ ▓ ▓┃    ┃ ▓▓▓▓     ▓▓▓▓▓  ▓▓▓▓░          ┃
┃▓▓ ▓▓  ▓   ▓ ▓  ▓▓▓   ▓    ▓▓   ┃    ┃ ▓▓▓▓     ▓▓▓    ▓▓          ░  ┃
┃  ▓▓   ▓ ▓▓▓▓  ▓▓      ▓▓  ▓ ▓  ┃    ┃  ▓▓   ▓▓▓▓▓▓               ░░  ┃
┃  ▓  ▓  ▓▓ ▓▓ ▓    ▓ ▓    ▓▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓             ▓▓▓▓  ┃
┃     ▓▓▓▓▓▓▓▓  ▓▓   ▓ ▓▓▓ ▓  ▓ ▓┃    ┃      ▓▓▓▓▓▓▓             ▓▓▓▓  ┃
┃ ▓▓▓  ▓ ▓▓▓  ▓  ▓▓ ▓      ▓▓ ▓▓ ┃    ┃      ▓▓▓▓▓▓▓   ▓▓▓▓      ▓▓▓▓  ┃
┃▓      ▓▓▓▓▓▓▓  ▓ ▓ ▓   ▓▓▓▓▓▓  ┃    ┃      ▓▓▓▓▓▓▓   ▓▓▓▓▓    ▓▓▓▓▓▓ ┃
┃    ▓▓▓ ▓▓▓ ▓ ▓ ▓▓▓▓ ▓▓  ▓▓▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓ ┃
┃▓     ▓  ▓   ▓▓▓  ▓▓▓   ▓ ▓▓▓  ▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓ ┃
┃▓▓     ▓▓▓▓▓▓  ▓▓▓▓ ▓▓      ▓▓▓▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓ ┃
┃▓ ▓ ▓ ▓▓ ▓  ▓ ▓ ▓    ▓   ▓   ▓  ┃    ┃       ▓▓▓    ░░   ▓▓▓          ┃
┃▓▓      ▓▓     ▓  ▓▓ ▓ ▓  ▓▓▓   ┃    ┃       ▓▓▓    ░░   ░░░          ┃
┃   ▓   ▓ ▓▓   ▓▓ ▓▓ ▓▓  ▓      ▓┃    ┃       ▓▓▓▓   ▓▓▓▓▓░░░          ┃
┃▓  ▓  ▓  ▓▓▓ ▓▓▓▓▓▓▓  ▓  ▓▓  ▓ ▓┃    ┃       ▓▓▓▓   ▓▓▓▓▓░░░          ┃
┃  ▓▓▓▓ ▓   ▓      ▓ ▓ ▓  ▓ ▓▓   ┃    ┃  ▓▓▓  ░░░░          ▓▓         ┃
┃▓▓▓▓▓   ▓ ▓          ▓▓   ▓ ▓  ▓┃    ┃▓▓▓▓▓  ░░░░          ▓▓         ┃
┃▓▓  ▓  ▓▓▓▓▓▓    ▓ ▓ ▓   ▓   ▓  ┃    ┃▓▓▓▓   ▓▓▓▓▓▓             ░     ┃
┃ ▓ ▓    ▓▓▓▓▓▓ ▓▓▓ ▓   ▓ ▓▓▓▓   ┃    ┃▓▓▓▓   ▓▓▓▓▓▓  ▓▓       ▓▓▓     ┃
┃▓▓▓▓ ▓▓▓ ▓     ▓   ▓▓  ▓▓▓▓     ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓      ▓▓▓▓     ┃
┃▓▓ ▓ ▓▓▓▓ ▓▓▓ ▓▓ ▓ ▓  ▓▓▓ ▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓     ┃
┃  ▓▓  ▓   ▓ ▓▓▓ ▓▓  ▓ ▓▓▓▓▓▓ ▓  ┃    ┃   ▓▓▓▓▓   ▓▓▓▓▓▓     ▓▓▓▓▓     ┃
┃ ▓ ▓ ▓▓▓ ▓  ▓ ▓ ▓ ▓▓ ▓   ▓▓ ▓ ▓▓┃    ┃    ▓▓▓▓    ▓▓▓          ▓▓   ▓▓┃
┃▓▓  ▓  ▓ ▓ ▓▓ ▓  ▓   ▓▓▓      ▓▓┃    ┃                              ▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓  ▓ ▓▓  ▓     ▓▓▓   ▓ ▓▓▓   ▓ ┃    ┃                ▓▓▓      ▓▓     ┃
┃▓ ▓▓▓   ▓ ▓ ▓▓▓▓▓▓▓   ▓   ▓ ▓  ▓┃    ┃   ▓▓           ▓▓▓      ▓▓▓    ┃
┃▓▓ ▓▓ ▓▓     ▓   ▓▓▓▓▓▓  ▓▓▓    ┃    ┃  ░▓▓            ▓▓░     ▓▓▓    ┃
┃▓  ▓   ▓ ▓▓▓   ▓    ▓  ▓ ▓ ▓  ▓ ┃    ┃   ░░    ▓▓▓            ▓▓▓▓    ┃
┃▓   ▓   ▓▓ ▓    ▓▓   ▓ ▓▓▓▓▓  ▓ ┃    ┃   ░░    ▓▓▓           ▓▓▓▓▓    ┃
┃  ▓▓▓▓▓▓ ▓ ▓▓  ▓  ▓▓   ▓     ▓  ┃    ┃   ▓▓▓▓▓               ▓        ┃
┃   ▓▓▓▓▓▓  ▓ ▓ ▓  ▓   ▓▓   ▓▓  ▓┃    ┃  ▓▓▓▓▓▓          ▓▓  ▓▓   ▓▓▓  ┃
┃▓ ▓▓     ▓▓  ▓  ▓ ▓▓ ▓▓▓▓ ▓▓▓▓▓ ┃    ┃ ▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓▓▓▓▓▓▓  ▓▓▓ ▓   ▓▓ ▓ ▓▓▓▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓    ▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓▓▓   ▓    ▓▓▓▓     ▓   ▓▓▓▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓    ▓▓▓     ░░   ▓▓▓▓▓▓  ┃
┃ ▓▓ ▓▓▓  ▓▓      ▓ ▓  ▓  ▓▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓  ▓▓        ░░    ▓▓▓▓▓▓ ┃
┃ ▓  ▓ ▓▓▓▓▓ ▓  ▓ ▓ ▓▓  ▓  ▓▓▓  ▓┃    ┃    ▓▓▓▓▓▓▓        ▓▓    ▓▓▓▓▓▓ ┃
┃▓   ▓▓▓▓    ▓     ▓ ▓▓   ▓▓▓ ▓▓▓┃    ┃    ▓▓▓▓▓          ▓▓▓   ▓▓▓▓▓▓ ┃
┃▓ ▓    ▓ ▓   ▓▓▓▓   ▓▓▓   ▓▓▓   ┃    ┃▓▓     ▓▓    ▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓ ┃
┃▓▓▓▓▓  ▓▓   ▓▓ ▓▓▓▓▓    ▓▓▓▓▓▓▓▓┃    ┃▓▓▓▓   ▓▓    ▓▓▓▓░░░     ▓▓▓▓▓▓ ┃
┃ ▓▓    ▓▓▓   ▓ ▓   ▓ ▓▓   ▓ ▓▓ ▓┃    ┃ ▓▓▓   ▓▓    ▓▓▓▓░░      ▓▓▓▓▓▓ ┃
┃ ▓▓▓▓▓ ▓▓ ▓  ▓▓ ▓ ▓  ▓  ▓▓▓  ▓  ┃    ┃ ▓▓▓   ▓▓    ▓▓         ▓▓▓▓▓   ┃
┃▓▓       ▓  ▓ ▓ ▓ ▓▓  ▓▓▓  ▓ ▓  ┃    ┃▓▓▓▓         ▓▓    ▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓▓ ▓▓▓  ▓▓▓▓     ▓▓▓    ▓ ▓ ▓ ┃    ┃▓▓▓▓▓    ▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓▓ ▓ ▓▓▓  ▓▓▓     ▓▓ ▓▓▓    ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓      ┃
┃ ▓▓  ▓▓▓▓  ▓ ▓  ▓▓ ▓▓  ▓▓▓  ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓      ┃
┃▓  ▓▓▓ ▓ ▓▓ ▓   ▓ ▓▓ ▓▓ ▓  ▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ▓▓▓  ┃
┃ ▓ ▓  ▓ ▓▓  ▓  ▓▓ ▓ ▓ ▓▓   ▓ ▓  ┃    ┃       ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓   ▓▓▓  ┃
┃▓▓  ▓ ▓   ▓ ▓▓   ▓ ▓▓▓ ▓ ▓▓▓ ▓  ┃    ┃           ░░   ▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓   ▓ ▓▓ ▓  ▓▓▓▓ ▓▓▓  ▓▓▓▓▓  ▓┃    ┃            ░▓▓   ▓▓▓▓▓▓▓▓▓▓▓   ┃
┃ ▓ ▓  ▓  ▓  ▓▓        ▓▓▓▓▓ ▓   ┃    ┃             ▓▓      ▓▓▓▓▓▓▓    ┃
┃ ▓  ▓  ▓  ▓  ▓▓ ▓    ▓▓ ▓▓▓▓   ▓┃    ┃             ▓▓      ▓▓▓▓▓▓▓    ┃
┃▓     ▓   ▓▓ ▓▓ ▓▓▓  ▓ ▓▓▓▓▓ ▓ ▓┃    ┃          ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓  ┃
┃▓   ▓ ▓▓▓  ▓▓ ▓▓▓ ▓▓  ▓▓  ▓▓▓ ▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ▓▓▓▓▓ ┃
┃▓▓ ▓▓  ▓▓▓▓ ▓ ▓  ▓▓   ▓▓  ▓ ▓▓  ┃    ┃▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓  ▓   ▓▓  ▓▓▓▓▓ ┃
┃ ▓ ▓      ▓▓▓ ▓▓   ▓ ▓   ▓ ▓ ▓▓▓┃    ┃▓▓▓▓▓     ▓▓▓▓▓   ▓▓       ▓▓▓▓ ┃
┃▓▓▓▓▓  ▓▓ ▓▓▓▓▓  ▓▓▓▓▓   ▓▓  ▓  ┃    ┃ ▓▓▓      ▓▓▓▓▓   ▓▓            ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓▓▓ ▓▓ ▓  ▓   ▓▓▓▓ ▓▓▓▓▓▓▓  ▓ ┃    ┃   ▓▓▓           ▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓  ▓▓  ▓  ▓  ▓  ▓▓▓▓▓ ▓▓  ▓▓  ▓┃    ┃   ▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓  ▓ ▓▓▓▓▓ ▓▓▓▓    ▓ ▓   ▓ ▓▓▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓     ▓▓▓  ┃
┃▓  ▓▓  ▓▓ ▓  ▓▓  ▓ ▓▓▓▓     ▓▓ ▓┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓      ▓▓  ┃
┃   ▓  ▓ ▓▓▓▓▓     ▓▓   ▓▓▓▓    ▓┃    ┃   ▓▓  ▓▓▓▓▓▓     ▓▓    ▓▓      ┃
┃▓▓ ▓▓  ▓▓▓ ▓▓ ▓▓▓▓ ▓    ▓▓   ▓▓ ┃    ┃   ▓▓  ▓▓▓▓▓▓    ▓▓▓    ▓▓      ┃
┃  ▓▓▓  ▓ ▓▓     ▓  ▓▓▓   ▓  ▓▓  ┃    ┃   ▓▓   ▓▓▓▓    ▓▓▓▓            ┃
┃    ▓▓   ▓▓▓  ▓▓ ▓▓▓  ▓▓      ▓▓┃    ┃         ▓▓▓   ▓▓▓▓▓  ▓▓      ▓▓┃
┃▓▓    ▓▓    ▓▓ ▓  ▓▓ ▓▓▓ ▓    ▓▓┃    ┃      ▓▓       ▓▓▓▓▓  ▓▓      ▓▓┃
┃ ▓  ▓ ▓▓▓ ▓▓  ▓ ▓▓▓▓  ▓ ▓▓▓ ▓  ▓┃    ┃      ▓▓       ▓▓▓▓▓            ┃
┃▓ ▓▓    ▓  ▓ ▓  ▓▓ ▓     ▓ ▓  ▓ ┃    ┃ ▓▓▓▓          ▓▓▓▓      ▓▓▓    ┃
┃▓▓ ▓▓   ▓▓ ▓  ▓▓  ▓      ▓▓▓ ▓▓ ┃    ┃▓▓▓▓▓          ▓▓        ▓▓▓▓▓▓ ┃
┃▓ ▓▓▓▓ ▓▓  ▓▓  ▓▓ ▓    ▓▓   ▓▓▓▓┃    ┃▓▓▓▓▓      ▓▓  ▓▓           ▓▓▓ ┃
┃▓ ▓ ▓ ▓    ▓▓ ▓ ▓ ▓   ▓ ▓ ▓ ▓ ▓ ┃    ┃▓▓▓▓▓      ▓▓               ▓▓▓ ┃
┃ ▓▓     ▓▓          ▓  ▓ ▓  ▓ ▓ ┃    ┃▓▓▓▓                        ▓   ┃
┃▓ ▓▓▓ ▓▓ ▓ ▓  ▓ ▓ ▓ ▓▓▓ ▓▓ ▓▓   ┃    ┃                           ▓▓   ┃
┃ ▓    ▓ ▓  ▓▓ ▓ ▓▓▓  ▓     ▓▓▓▓ ┃    ┃            ▓▓▓▓▓▓▓        ▓▓▓  ┃
┃▓▓ ▓▓▓ ▓  ▓▓ ▓▓▓▓ ▓▓     ▓▓ ▓   ┃    ┃ ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓       ▓▓▓  ┃
┃ ▓▓ ▓▓▓▓▓  ▓▓▓ ▓▓▓▓▓ ▓ ▓    ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓┃
┃ ▓ ▓▓  ▓▓▓▓▓▓▓▓ ▓  ▓▓▓     ▓  ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        ▓▓┃
┃ ▓ ▓▓ ▓  ▓     ▓▓▓▓   ▓▓▓  ▓  ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓      ▓▓┃
┃▓ ▓▓ ▓ ▓▓ ▓▓▓▓  ▓   ▓▓▓ ▓ ▓ ▓  ▓┃    ┃ ▓▓▓▓▓▓        ▓▓▓  ▓▓▓▓▓       ┃
┃▓▓ ▓▓▓▓  ▓  ▓  ▓▓▓▓ ▓  ▓ ▓   ▓▓ ┃    ┃  ▓▓▓▓▓        ▓▓▓  ░▓▓▓▓▓      ┃
┃▓   ▓ ▓▓   ▓ ▓▓ ▓ ▓  ▓ ▓ ▓▓  ▓ ▓┃    ┃    ▓▓▓         ▓▓  ▓▓▓▓▓▓▓     ┃
┃▓▓   ▓   ▓▓▓   ▓▓▓ ▓▓ ▓ ▓▓▓  ▓▓ ┃    ┃     ▓▓         ▓▓▓▓▓▓▓▓▓▓▓  ▓▓ ┃
┃▓   ▓▓ ▓▓     ▓ ▓  ▓ ▓▓ ▓▓ ▓ ▓  ┃    ┃     ▓▓           ▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓    ▓▓   ▓▓    ▓▓ ▓▓ ▓▓ ▓ ▓▓▓▓▓┃    ┃     ▓▓            ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃ ▓    ▓ ▓▓ ▓▓   ▓   ▓ ▓▓▓ ▓▓   ▓┃    ┃      ▓               ▓▓▓▓▓▓▓   ┃
┃ ▓▓   ▓▓  ▓   ▓▓  ▓▓  ▓  ▓ ▓ ▓▓ ┃    ┃      ▓▓                   ▓▓   ┃
┃ ▓ ▓ ▓▓   ▓   ▓ ▓▓   ▓ ▓   ▓▓  ▓┃    ┃      ▓▓         ▓▓        ▓▓   ┃
┃▓     ▓▓▓▓▓ ▓  ▓ ▓▓ ▓   ▓  ▓▓   ┃    ┃      ▓▓         ▓▓        ▓▓   ┃
┃▓ ▓ ▓  ▓ ▓  ▓   ▓ ▓  ▓▓     ▓ ▓ ┃    ┃                                ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓ ▓   ▓ ▓▓▓▓   ▓ ▓  ▓▓▓  ▓ ▓▓ ┃    ┃           ▓▓          ▓▓       ┃
┃▓▓▓▓    ▓  ▓▓ ▓▓ ▓ ▓▓  ▓▓ ▓  ▓  ┃    ┃ ▓▓▓▓      ▓▓          ▓▓       ┃
┃▓ ▓▓▓▓▓▓ ▓ ▓   ▓  ▓       ▓▓▓  ▓┃    ┃ ▓▓▓▓▓▓                         ┃
┃   ▓ ▓ ▓   ▓     ▓       ▓   ▓  ┃    ┃  ▓▓▓▓▓                         ┃
┃ ▓▓▓▓ ▓  ▓  ▓  ▓▓▓ ▓   ▓  ▓    ▓┃    ┃  ▓▓▓▓▓▓       ▓▓▓              ┃
┃▓  ▓  ▓▓  ▓   ▓▓▓ ▓  ▓▓ ▓ ▓   ▓▓┃    ┃      ▓▓▓      ▓▓▓    ▓▓▓       ┃
┃▓  ▓  ▓▓▓▓▓   ▓  ▓▓▓▓ ▓▓ ▓ ▓▓  ▓┃    ┃      ▓▓▓▓▓        ▓▓▓▓▓▓░░▓▓   ┃
┃    ▓▓▓ ▓  ▓    ▓  ▓▓  ▓▓▓ ▓▓   ┃    ┃    ▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓░▓▓   ┃
┃ ▓▓ ▓▓ ▓▓▓▓▓▓   ▓    ▓▓        ▓┃    ┃ ▓▓ ▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓      ┃
┃ ▓▓  ▓  ▓▓▓▓   ▓▓▓ ▓ ▓▓ ▓▓ ▓ ▓ ▓┃    ┃ ▓▓ ▓▓▓▓▓▓▓▓   ▓▓   ▓▓▓▓▓▓      ┃
┃    ▓▓▓▓   ▓ ▓▓▓    ▓ ▓▓▓▓ ▓ ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓   ┃
┃▓▓  ▓ ▓ ▓ ▓ ▓▓ ▓▓  ▓▓▓ ▓▓ ▓▓▓ ▓▓┃    ┃    ▓▓     ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓▓ ▓     ▓▓   ▓▓ ▓ ▓▓▓▓▓▓ ▓▓  ┃    ┃ ▓▓▓▓      ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓▓▓▓ ▓ ▓ ▓ ▓    ▓▓ ▓▓ ▓   ▓▓▓▓┃    ┃ ▓▓▓▓     ▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓▓ ┃
┃▓▓▓▓      ▓▓ ▓   ▓▓ ▓ ▓▓▓  ▓▓▓ ▓┃    ┃▓▓▓▓      ▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓▓ ┃
┃▓▓    ▓▓  ▓ ▓  ▓▓▓▓ ▓▓▓    ▓  ▓ ┃    ┃▓▓        ▓▓▓   ▓▓▓▓▓▓▓    ▓▓▓▓ ┃
┃▓▓ ▓▓▓▓  ▓▓▓▓▓  ▓▓ ▓ ▓▓   ▓▓ ▓▓ ┃    ┃▓▓      ▓▓▓▓▓▓  ▓▓▓▓▓▓▓   ▓▓▓▓▓ ┃
┃       ▓▓▓   ▓  ▓  ▓   ▓▓ ▓ ▓ ▓ ┃    ┃        ▓▓▓▓▓▓   ▓▓▓▓▓▓▓  ▓▓▓▓  ┃
┃▓ ▓▓▓   ▓ ▓ ▓▓▓  ▓▓▓▓▓▓▓  ▓   ▓ ┃    ┃        ▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓       ┃
┃    ▓ ▓▓ ▓▓ ▓  ▓▓ ▓▓   ▓▓▓ ▓  ▓▓┃    ┃        ▓▓▓      ▓▓▓  ▓▓▓▓    ▓▓┃
┃  ▓  ▓  ▓▓   ▓▓    ▓  ▓   ▓▓▓▓ ▓┃    ┃        ▓▓▓      ░░      ▓▓▓  ▓▓┃
┃▓▓   ▓  ▓▓▓▓     ▓▓  ▓  ▓▓▓    ▓┃    ┃ ▓▓     ▓▓▓▓     ░░      ▓▓▓  ▓▓┃
┃ ▓▓▓▓ ▓  ▓▓▓ ▓▓▓ ▓  ▓▓▓▓ ▓▓▓ ▓ ▓┃    ┃ ▓▓▓     ▓▓▓▓▓▓  ▓▓▓▓▓▓  ▓▓▓  ▓▓┃
┃▓▓▓▓ ▓▓   ▓▓▓▓   ▓▓▓▓      ▓  ▓▓┃    ┃ ▓▓▓      ▓▓▓▓▓  ▓▓▓▓▓▓      ▓▓▓┃
┃    ▓      ▓ ▓▓▓▓▓ ▓▓▓▓ ▓   ▓▓▓▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓┃
┃▓ ▓    ▓▓▓ ▓▓▓▓▓  ▓▓ ▓▓   ▓ ▓▓▓▓┃    ┃        ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓┃
┃▓▓▓ ▓▓  ▓▓  ▓▓▓ ▓▓ ▓   ▓▓ ▓   ▓▓┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓           ▓▓┃
┃▓    ▓▓▓ ▓▓▓▓ ▓ ▓ ▓ ▓ ▓  ▓  ▓ ▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓            ▓▓┃
┃▓  ▓ ▓▓   ▓▓▓▓  ▓▓ ▓     ▓    ▓▓┃    ┃     ▓▓   ▓▓▓▓▓▓▓▓            ▓▓┃
┃▓ ▓ ▓  ▓  ▓ ▓ ▓▓ ▓       ▓ ▓   ▓┃    ┃    ▓▓    ▓▓▓▓▓▓▓▓              ┃
┃  ▓ ▓▓  ▓▓▓▓   ▓ ▓ ▓ ▓▓▓  ▓ ▓   ┃    ┃  ▓▓▓▓  ▓▓▓▓▓                   ┃
┃ ▓▓▓▓▓  ▓▓▓▓▓▓ ▓       ▓ ▓   ▓▓ ┃    ┃  ▓▓▓▓  ▓▓▓▓▓                   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃   ▓▓▓▓▓  ▓ ▓▓ ▓▓  ▓▓▓ ▓▓▓▓▓▓▓▓ ┃    ┃    ▓▓▓▓           ▓▓           ┃
┃▓   ▓▓▓▓   ▓    ▓▓▓▓▓  ▓   ▓    ┃    ┃    ▓▓▓▓        ▓▓▓▓▓           ┃
┃       ▓ ▓▓▓ ▓▓ ▓▓   ▓   ▓    ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓             ┃
┃ ▓ ▓ ▓▓ ▓▓▓ ▓▓▓▓▓  ▓▓  ▓     ▓  ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓               ┃
┃ ▓▓ ▓▓▓▓ ▓▓   ▓▓  ▓▓   ▓▓▓▓  ▓  ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓      ┃
┃ ▓ ▓ ▓▓▓▓▓ ▓▓▓▓▓▓      ▓ ▓  ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓      ┃
┃   ▓▓ ▓▓▓▓ ▓ ▓       ▓▓▓ ▓ ▓  ▓▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓      ┃
┃ ▓▓▓▓  ▓▓▓ ▓▓▓ ▓▓  ▓ ▓▓ ▓▓ ▓ ▓ ▓┃    ┃ ▓▓▓▓  ▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓      ┃
┃ ▓▓▓▓   ▓     ▓ ▓ ▓▓   ▓  ▓   ▓ ┃    ┃ ▓▓▓▓  ░░▓▓▓▓▓▓▓▓▓▓▓            ┃
┃  ▓ ▓ ▓▓ ▓ ▓▓▓▓▓▓ ▓▓▓ ▓   ▓    ▓┃    ┃ ▓▓     ░░▓▓▓▓▓▓▓▓▓▓            ┃
┃▓▓    ▓   ▓ ▓    ▓   ▓▓▓ ▓▓▓▓▓ ▓┃    ┃▓▓       ░░░░  ▓▓▓      ▓▓▓▓▓▓▓▓┃
┃▓▓ ▓▓▓▓ ▓▓ ▓  ▓ ▓▓     ▓ ▓ ▓ ▓▓▓┃    ┃▓▓       ░░░░           ▓▓▓▓▓▓▓▓┃
┃▓▓      ▓ ▓▓▓▓ ▓▓  ▓▓▓  ▓▓▓▓ ▓ ▓┃    ┃▓▓       ▓▓▓▓      ▓▓   ▓▓▓▓▓▓▓▓┃
┃ ▓ ▓▓ ▓   ▓▓       ▓▓   ▓ ▓ ▓▓▓▓┃    ┃▓▓▓▓▓▓   ▓▓▓▓      ▓▓   ▓▓▓▓▓▓▓▓┃
┃▓▓▓ ▓▓▓▓▓▓▓ ▓▓▓    ▓▓  ▓▓▓  ▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓      ▓▓▓▓ ┃
┃ ▓ ▓   ▓   ▓  ▓▓   ▓▓ ▓    ▓▓▓ ▓┃    ┃ ▓▓▓▓      ▓▓▓▓    ▓▓      ▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓   ▓▓▓▓   ▓▓  ▓▓   ▓ ▓▓ ┃    ┃ ▓▓▓▓       ▓▓▓▓  ▓▓▓▓▓▓   ▓▓▓▓ ┃
┃ ▓▓▓▓       ▓▓▓▓▓ ▓▓▓▓▓▓▓  ▓▓▓  ┃    ┃ ▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓ ┃
┃    ▓▓▓ ▓▓   ▓▓ ▓▓▓ ▓▓  ▓▓  ▓▓▓▓┃    ┃    ▓▓      ▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓ ┃
┃▓▓     ▓▓   ▓▓ ▓▓▓  ▓▓    ▓▓   ▓┃    ┃       ▓▓   ▓▓▓▓▓▓▓▓▓▓     ▓▓▓  ┃
┃  ▓  ▓▓ ▓▓ ▓▓ ▓▓▓▓▓  ▓▓▓▓  ▓▓ ▓ ┃    ┃       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃ ▓▓▓▓ ▓   ▓▓  ▓▓▓▓ ▓▓  ▓▓▓▓   ▓ ┃    ┃  ▓▓▓    ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓    ┃
┃   ▓▓▓  ▓ ▓▓ ▓▓ ▓▓   ▓▓ ▓▓ ▓▓▓ ▓┃    ┃  ▓▓▓    ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓ ┃
┃▓ ▓ ▓   ▓▓▓▓▓ ▓▓▓▓  ▓▓  ▓▓ ▓ ▓▓ ┃    ┃  ▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓▓▓▓ ┃
┃ ▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓▓  ▓▓▓ ▓ ▓ ▓ ▓▓ ┃    ┃ ▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓▓ ┃
┃ ▓▓  ▓ ▓▓  ▓ ▓   ▓  ▓     ▓▓▓▓  ┃    ┃ ▓▓    ▓▓  ▓▓▓      ▓▓    ▓▓▓▓  ┃
┃     ▓   ▓  ▓▓  ▓   ▓▓ ▓   ▓▓   ┃    ┃           ▓▓▓      ▓▓▓   ▓▓▓   ┃
┃▓▓       ▓ ▓▓ ▓ ▓  ▓▓▓▓▓  ▓▓  ▓▓┃    ┃         ▓▓▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓   ┃
┃       ▓▓▓▓  ▓ ▓▓▓ ▓▓▓▓▓▓▓▓▓▓   ┃    ┃         ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓▓▓▓   ▓  ▓▓▓▓▓▓▓▓▓▓ ▓▓  ▓▓▓  ▓▓┃    ┃ ▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ┃
┃ ▓ ▓▓       ▓▓▓▓▓ ▓ ▓ ▓ ▓ ▓▓   ▓┃    ┃ ▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓┃
┃▓▓ ▓▓ ▓▓ ▓  ▓  ▓▓▓ ▓▓▓ ▓  ▓▓▓▓▓▓┃    ┃  ▓▓▓          ▓▓▓▓▓      ▓▓▓▓▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓   ▓▓▓▓▓▓    ▓ ▓    ▓▓▓▓▓▓▓▓▓┃    ┃ ▓▓      ▓▓▓           ▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓  ▓   ▓▓    ▓    ▓ ▓▓▓▓ ▓▓▓▓┃    ┃ ▓▓▓     ▓▓▓           ▓▓▓▓▓▓▓▓▓┃
┃▓▓ ▓▓   ▓ ▓▓        ▓ ▓   ▓▓ ▓  ┃    ┃ ▓▓▓▓    ▓▓▓           ▓▓▓▓▓▓▓▓ ┃
┃    ▓▓ ▓ ▓   ▓   ▓▓    ▓▓▓ ▓ ▓▓ ┃    ┃ ▓▓▓▓▓                 ▓▓▓▓▓▓▓▓ ┃
┃▓▓▓ ▓▓  ▓▓ ▓ ▓▓▓ ▓ ▓▓  ▓▓ ▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓       ▓▓        ▓▓▓▓▓▓▓▓ ┃
┃▓▓ ▓▓ ▓▓ ▓ ▓▓ ▓  ▓   ▓▓▓▓▓    ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓   ▓▓      ▓▓▓▓   ▓▓▓ ┃
┃ ▓   ▓ ▓▓     ▓▓     ▓▓    ▓▓▓  ┃    ┃    ▓▓▓▓▓▓    ▓▓     ▓▓     ▓▓  ┃
┃ ▓ ▓▓ ▓▓▓▓ ▓▓ ▓ ▓▓  ▓▓▓   ▓ ▓▓  ┃    ┃     ▓▓▓▓▓    ▓▓▓▓   ▓▓     ▓▓  ┃
┃ ▓ ▓ ▓▓ ▓▓    ▓▓▓▓ ▓ ▓  ▓ ▓▓ ▓▓▓┃    ┃     ▓▓▓▓▓    ▓▓▓▓   ▓▓  ▓▓▓▓▓▓▓┃
┃▓     ▓▓  ▓▓   ▓ ▓  ▓ ▓▓▓▓▓  ▓ ▓┃    ┃      ▓▓▓▓    ▓▓▓▓   ▓▓▓▓▓▓  ▓▓▓┃
┃   ▓ ▓ ▓ ▓   ▓▓▓▓▓▓ ▓ ▓  ▓  ▓ ▓▓┃    ┃      ░░     ▓▓▓▓▓    ▓▓▓    ▓▓▓┃
┃ ▓   ▓▓  ▓▓ ▓▓▓  ▓   ▓ ▓▓  ▓▓▓ ▓┃    ┃      ░░    ▓▓▓▓▓▓         ▓▓▓▓▓┃
┃▓▓     ▓    ▓▓▓▓▓ ▓   ▓    ▓▓▓▓▓┃    ┃▓▓    ░░    ▓▓▓▓▓▓         ▓▓▓▓▓┃
┃▓▓    ▓▓▓▓▓▓▓ ▓▓ ▓    ▓   ▓  ▓▓▓┃    ┃▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓           ▓▓▓┃
┃▓▓▓  ▓▓  ▓    ▓▓▓ ▓ ▓  ▓▓ ▓    ▓┃    ┃▓▓▓  ▓▓▓▓▓▓   ▓▓▓▓    ▓▓▓       ┃
┃▓▓▓▓ ▓▓ ▓▓ ▓   ▓ ▓▓▓  ▓▓▓       ┃    ┃▓▓▓▓ ▓▓▓▓▓▓   ░░▓▓▓░░▓▓▓▓       ┃
┃▓ ▓▓ ▓ ▓▓ ▓▓  ▓  ▓▓ ▓▓▓▓▓  ▓ ▓  ┃    ┃▓▓▓▓   ▓▓▓▓▓  ░░░▓▓░░▓▓▓▓       ┃
┃▓▓▓▓    ▓▓▓   ▓▓   ▓ ▓▓▓▓▓▓▓ ▓▓▓┃    ┃▓▓▓▓    ▓▓▓▓  ░░░░░░░▓▓▓▓       ┃
┃▓▓    ▓   ▓▓▓ ▓ ▓▓▓  ▓▓▓▓  ▓    ┃    ┃▓▓        ▓▓▓▓▓▓▓▓░░░▓▓▓▓       ┃
┃▓▓ ▓▓▓  ▓ ▓  ▓▓    ▓  ▓ ▓     ▓▓┃    ┃▓▓  ▓▓▓     ▓▓▓▓▓▓▓    ░░       ┃
┃▓    ▓▓ ▓   ▓▓▓▓ ▓▓ ▓  ▓ ▓▓ ▓▓ ▓┃    ┃    ▓▓▓▓    ▓▓▓▓▓▓▓    ░░       ┃
┃  ▓▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓ ▓   ▓    ▓  ┃    ┃   ▓▓▓▓▓░░▓▓▓▓▓▓▓▓▓    ░░       ┃
┃▓▓ ▓▓  ▓  ▓   ▓ ▓    ▓▓▓▓▓▓ ▓ ▓ ┃    ┃   ▓▓▓▓▓░░▓▓▓▓▓▓▓▓   ▓▓▓▓▓      ┃
┃   ▓▓▓ ▓ ▓▓▓▓▓▓  ▓▓ ▓▓  ▓     ▓▓┃    ┃  ▓▓▓   ░░▓▓▓▓▓▓▓▓   ▓▓▓▓▓      ┃
┃ ▓▓▓▓   ▓ ▓▓▓ ▓ ▓▓    ▓▓▓ ▓▓▓   ┃    ┃  ▓▓▓    ░▓▓▓▓▓        ▓▓▓▓▓▓   ┃
┃▓ ▓ ▓    ▓   ▓▓   ▓▓▓  ▓▓▓▓ ▓▓  ┃    ┃ ▓▓▓▓         ▓        ▓▓▓▓▓▓   ┃
┃▓ ▓ ▓ ▓▓▓▓▓   ▓     ▓  ▓ ▓    ▓ ┃    ┃▓▓▓▓▓         ▓                 ┃
┃▓▓▓ ▓   ▓     ▓▓  ▓▓  ▓   ▓ ▓   ┃    ┃▓▓▓▓▓         ▓▓                ┃
┃ ▓▓ ▓    ▓ ▓ ▓ ▓▓▓  ▓ ▓▓▓ ▓▓    ┃    ┃▓▓▓▓▓         ▓▓     ▓▓▓        ┃
┃▓▓  ▓▓     ▓       ▓▓▓▓▓  ▓  ▓  ┃    ┃▓▓  ▓▓               ▓▓▓        ┃
┃▓▓  ▓▓▓   ▓ ▓▓▓ ▓        ▓      ┃    ┃▓▓  ▓▓                          ┃
┃▓ ▓ ▓▓ ▓  ▓▓ ▓     ▓ ▓▓▓▓  ▓▓▓  ┃    ┃    ▓▓                          ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓ ▓   ▓ ▓▓▓ ▓▓ ▓    ▓▓    ▓ ▓ ▓┃    ┃         ▓▓▓                    ┃
┃▓ ▓  ▓▓ ▓▓ ▓ ▓ ▓▓▓ ▓  ▓▓▓▓ ▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓   ┃
┃  ▓ ▓▓▓   ▓▓  ▓▓ ▓▓▓▓▓  ▓▓▓▓ ▓ ▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓ ▓ ▓ ▓ ▓▓ ▓▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ┃
┃▓ ▓▓       ▓▓▓▓▓▓▓▓   ▓ ▓  ▓   ▓┃    ┃          ▓▓▓▓▓▓▓▓▓   ▓▓▓       ┃
┃    ▓▓    ▓▓▓ ▓  ▓▓▓  ▓▓▓    ▓ ▓┃    ┃          ▓▓▓▓▓▓▓▓▓   ▓▓▓       ┃
┃ ▓ ▓ ▓   ▓ ▓▓ ▓ ▓▓     ▓▓▓ ▓  ▓ ┃    ┃  ▓▓▓▓     ▓▓▓▓       ▓▓▓▓      ┃
┃▓▓▓ ▓▓▓   ▓  ▓▓    ▓▓▓ ▓▓▓ ▓▓▓  ┃    ┃▓▓▓▓▓▓             ▓▓▓▓▓▓▓      ┃
┃▓▓▓ ▓  ▓  ▓     ▓▓ ▓▓ ▓▓ ▓      ┃    ┃▓▓▓▓▓▓          ▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓ ▓▓ ▓▓▓  ▓ ▓▓▓▓▓▓ ▓▓ ▓▓  ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃ ▓▓  ▓▓ ▓▓ ▓▓▓ ▓▓▓ ▓   ▓ ▓▓▓▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓▓    ┃
┃▓ ▓ ▓ ▓ ▓   ▓▓▓   ▓▓▓      ▓  ▓ ┃    ┃  ▓▓▓▓▓▓▓▓  ▓▓▓  ▓▓      ▓▓▓    ┃
┃ ▓▓ ▓▓ ▓ ▓ ▓  ▓ ▓▓    ▓▓▓▓▓▓  ▓ ┃    ┃  ▓▓▓▓▓▓▓        ▓▓      ▓▓▓    ┃
┃   ▓▓▓▓▓▓ ▓ ▓    ▓▓▓ ▓     ▓ ▓ ▓┃    ┃    ▓▓▓▓         ▓▓       ▓▓    ┃
┃     ▓▓▓ ▓▓ ▓  ▓  ▓ ▓▓    ▓▓  ▓▓┃    ┃    ▓▓▓▓         ▓▓       ▓▓    ┃
┃    ▓▓▓ ▓ ▓   ▓▓ ▓▓▓ ▓     ▓▓ ▓ ┃    ┃     ▓▓▓       ▓▓▓▓             ┃
┃▓▓▓▓  ▓▓▓  ▓▓▓ ▓▓▓▓ ▓ ▓ ▓ ▓     ┃    ┃ ▓▓   ▓▓       ▓▓▓▓             ┃
┃  ▓     ▓    ▓  ▓▓  ▓     ▓  ▓  ┃    ┃ ▓▓             ▓▓▓             ┃
┃ ▓▓ ▓ ▓▓  ▓       ▓   ▓▓▓ ▓▓▓▓▓▓┃    ┃ ▓▓                    ▓▓▓▓▓▓▓  ┃
┃▓▓   ▓▓  ▓    ▓ ▓ ▓ ▓▓ ▓▓▓▓▓   ▓┃    ┃ ▓▓                   ▓▓▓▓▓▓▓▓  ┃
┃▓ ▓▓  ▓  ▓ ▓  ▓▓▓▓   ▓ ▓▓▓  ▓▓▓ ┃    ┃              ▓▓▓▓    ▓▓▓▓▓▓▓▓  ┃
┃     ▓ ▓▓▓    ▓▓▓▓    ▓▓▓ ▓ ▓▓  ┃    ┃      ▓▓▓▓    ▓▓▓▓    ▓▓▓▓▓▓▓▓  ┃
┃▓ ▓▓  ▓▓▓▓▓      ▓ ▓  ▓ ▓ ▓▓▓▓  ┃    ┃      ▓▓▓▓            ▓▓▓▓▓▓▓▓  ┃
┃▓▓ ▓   ▓▓  ▓      ▓  ▓▓▓▓▓ ▓ ▓▓▓┃    ┃▓▓▓▓  ▓▓▓             ▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓▓▓▓▓▓   ▓    ▓▓  ▓  ▓▓▓▓  ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓            ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓▓▓ ▓▓▓    ▓    ▓▓  ▓▓▓▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓           ▓▓▓▓▓▓▓▓▓▓▓┃
┃▓  ▓▓   ▓ ▓ ▓  ▓ ▓   ▓ ▓▓▓ ▓ ▓ ▓┃    ┃   ▓▓▓  ▓▓▓▓         ▓▓▓▓▓▓▓    ┃
┃   ▓▓▓   ▓ ▓▓▓▓    ▓ ▓▓         ┃    ┃   ▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓▓▓▓░     ┃
┃▓▓▓▓ ▓▓ ▓ ▓▓  ▓▓  ▓  ▓ ▓▓ ▓▓▓▓▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓   ┃
┃▓   ▓ ▓▓▓▓▓▓ ▓▓▓  ▓▓▓  ▓ ▓    ▓ ┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓▓▓   ┃
┃   ▓ ▓   ▓▓ ▓▓ ▓ ▓▓  ▓ ▓▓▓▓▓ ▓  ┃    ┃        ▓▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓▓    ┃
┃       ▓▓ ▓▓▓▓  ▓▓  ▓  ▓▓ ▓▓▓  ▓┃    ┃         ▓▓▓▓▓         ▓▓▓▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓ ▓ ▓   ▓ ▓   ▓▓  ▓▓▓ ▓ ▓  ┃    ┃  ▓▓▓▓▓            ▓▓           ┃
┃▓▓ ▓▓▓▓▓ ▓    ▓ ▓▓ ▓▓▓ ▓  ▓▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓         ▓▓▓▓▓    ▓▓▓▓▓▓┃
┃  ▓▓  ▓▓ ▓▓  ▓   ▓▓  ▓▓   ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓         ▓▓▓▓▓    ▓▓▓▓▓▓┃
┃▓▓ ▓▓▓▓     ▓▓▓▓ ▓▓▓▓▓  ▓▓▓▓    ┃    ┃ ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓    ┃
┃ ▓  ▓▓  ▓  ▓▓   ▓▓ ▓ ▓ ▓▓▓▓   ▓ ┃    ┃    ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓     ┃
┃ ▓        ▓▓ ▓▓ ▓▓▓ ▓▓▓  ▓     ▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓ ▓▓ ▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓▓▓  ▓ ▓   ▓┃    ┃      ▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓▓▓         ┃
┃▓▓   ▓ ▓▓ ▓▓▓  ▓▓ ▓▓   ▓   ▓ ▓  ┃    ┃      ▓▓▓ ▓▓▓▓▓▓▓▓▓▓       ▓▓   ┃
┃▓  ▓▓  ▓     ▓▓▓▓▓▓   ▓    ▓▓ ▓▓┃    ┃       ░░     ▓▓▓▓▓▓       ▓▓▓▓ ┃
┃▓  ▓ ▓▓ ▓▓▓    ▓ ▓▓ ▓   ▓▓▓ ▓▓▓ ┃    ┃       ░░     ▓▓▓▓▓▓       ▓▓▓▓ ┃
┃   ▓▓  ▓  ▓▓▓▓ ▓▓ ▓▓▓ ▓ ▓  ▓▓▓ ▓┃    ┃     ▓▓░░ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓┃
┃  ▓  ▓▓▓▓ ▓  ▓▓▓▓ ▓▓ ▓ ▓▓  ▓ ▓▓▓┃    ┃     ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓┃
┃   ▓ ▓▓   ▓▓  ▓▓▓▓ ▓▓▓▓▓▓  ▓ ▓▓ ┃    ┃     ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓┃
┃▓ ▓   ▓   ▓ ▓ ▓▓  ▓▓▓▓    ▓ ▓  ▓┃    ┃     ▓▓   ░▓▓▓▓▓  ▓▓▓▓          ┃
┃▓   ▓▓ ▓▓  ▓ ▓ ▓  ▓▓▓   ▓ ▓ ▓  ▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓           ┃
┃ ▓ ▓▓▓▓▓▓▓▓▓▓ ▓   ▓▓▓ ▓▓      ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓       ┃
┃▓▓▓▓    ▓▓▓▓ ▓     ▓▓  ▓▓▓▓▓▓ ▓▓┃    ┃ ▓▓▓▓   ▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓▓▓    ┃
┃  ▓ ▓▓    ▓▓ ▓▓▓▓ ▓  ▓    ▓▓    ┃    ┃ ▓▓▓▓     ▓▓▓▓▓▓▓  ▓▓    ▓▓▓▓   ┃
┃ ▓▓▓  ▓   ▓▓▓▓▓▓▓  ▓▓▓▓ ▓▓ ▓▓▓▓ ┃    ┃ ▓▓▓▓     ▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓   ┃
┃▓▓▓ ▓▓▓▓▓▓▓   ▓▓   ▓▓▓    ▓   ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓  ▓▓▓   ▓▓▓    ┃
┃     ▓▓▓     ▓▓▓▓▓   ▓▓ ▓▓▓ ▓ ▓ ┃    ┃     ▓▓▓▓    ▓▓▓▓▓  ▓▓   ▓▓▓    ┃
┃▓▓▓  ▓  ▓   ▓▓ ▓▓▓  ▓▓    ▓▓    ┃    ┃ ▓▓  ▓▓▓░    ▓▓▓▓▓       ▓▓▓    ┃
┃▓ ▓▓▓  ▓ ▓ ▓ ▓▓▓▓▓▓▓   ▓▓▓▓▓ ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓░░░░▓▓▓▓▓     ▓▓▓▓▓▓▓▓ ┃
┃ ▓▓ ▓▓▓ ▓▓▓▓▓ ▓     ▓  ▓  ▓▓▓▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓░░░        ▓▓▓▓▓▓▓▓ ┃
┃     ▓   ▓     ▓  ▓  ▓ ▓▓▓▓   ▓ ┃    ┃     ▓▓▓▓▓▓▓▓░░        ▓▓▓▓▓▓▓▓ ┃
┃ ▓▓  ▓▓▓▓▓ ▓▓▓▓   ▓▓▓ ▓▓▓  ▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ▓▓▓   ▓▓ ┃
┃▓ ▓ ▓ ▓  ▓▓▓▓▓▓ ▓ ▓▓   ▓ ▓   ▓▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓        ▓▓ ┃
┃▓ ▓▓▓▓▓▓ ▓      ▓  ▓▓▓   ▓▓ ▓▓▓ ┃    ┃ ▓▓▓▓▓▓▓           ▓▓      ▓▓▓▓ ┃
┃ ▓▓   ▓ ▓   ▓▓▓    ▓  ▓  ▓ ▓  ▓▓┃    ┃ ▓▓  ░░░     ▓▓          ▓▓▓▓▓▓▓┃
┃ ▓   ▓ ▓   ▓ ▓▓ ▓▓▓     ▓▓▓▓▓ ▓▓┃    ┃     ░░░     ▓▓  ▓▓▓     ▓▓▓▓▓▓▓┃
┃▓    ▓▓▓         ▓▓▓▓▓▓▓ ▓▓ ▓  ▓┃    ┃     ▓▓▓         ▓▓▓     ▓▓▓▓   ┃
┃  ▓▓▓▓ ▓▓▓▓▓   ▓▓       ▓▓ ▓▓▓▓ ┃    ┃     ▓▓▓                 ▓▓▓▓   ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃      ▓  ▓  ▓▓▓▓▓ ▓  ▓▓▓     ▓▓▓┃    ┃             ▓▓▓                ┃
┃    ▓ ▓▓▓   ▓ ▓▓ ▓ ▓▓▓   ▓     ▓┃    ┃             ▓▓▓                ┃
┃▓   ▓     ▓   ▓ ▓ ▓       ▓▓▓▓ ▓┃    ┃                                ┃
┃ ▓▓▓   ▓ ▓▓▓▓  ▓     ▓   ▓ ▓   ▓┃    ┃▓▓▓▓     ▓▓▓▓                   ┃
┃▓▓ ▓ ▓▓  ▓▓▓▓▓   ▓    ▓ ▓▓▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓           ▓▓▓     ┃
┃▓ ▓▓ ▓▓ ▓ ▓▓▓  ▓▓▓ ▓▓ ▓ ▓▓▓ ▓▓  ┃    ┃▓▓▓▓▓▓▓  ▓▓▓▓     ▓▓▓   ▓▓▓▓    ┃
┃▓   ▓▓▓     ▓ ▓ ▓  ▓▓  ▓ ▓▓▓ ▓ ▓┃    ┃▓▓  ▓▓▓     ▓▓░░▓▓▓▓▓   ▓▓▓▓▓▓  ┃
┃▓▓▓ ▓ ▓ ▓ ▓ ▓▓▓  ▓▓▓   ▓▓▓  ▓▓▓ ┃    ┃    ▓▓▓     ▓▓░░▓▓▓▓▓   ▓▓  ▓▓▓ ┃
┃ ▓   ▓▓ ▓▓     ▓▓▓▓ ▓   ▓▓  ▓  ▓┃    ┃  ▓▓▓▓▓         ▓▓▓▓▓   ▓▓  ▓▓▓ ┃
┃  ▓▓▓▓▓  ▓▓       ▓ ▓▓▓ ▓  ▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓           ▓▓▓▓     ▓▓▓▓ ┃
┃ ▓ ▓     ▓ ▓ ▓▓▓▓ ▓ ▓▓     ▓▓▓▓ ┃    ┃ ▓▓▓▓▓▓           ▓▓▓▓     ▓▓▓▓ ┃
┃▓  ▓▓▓▓▓▓ ▓▓   ▓   ▓▓▓▓  ▓▓  ▓▓ ┃    ┃ ▓▓▓▓▓   ░        ▓▓▓▓     ▓▓▓▓ ┃
┃▓▓▓ ▓  ▓     ▓   ▓▓  ▓  ▓  ▓▓▓▓ ┃    ┃ ▓▓▓▓             ▓▓▓▓    ▓▓▓▓▓ ┃
┃ ▓▓▓    ▓ ▓▓▓  ▓  ▓▓ ▓▓  ▓▓▓  ▓▓┃    ┃ ▓▓▓▓             ▓▓▓▓    ▓▓▓▓▓ ┃
┃    ▓ ▓  ▓▓  ▓▓    ▓ ▓    ▓▓▓▓▓ ┃    ┃ ▓▓▓▓               ░     ▓▓▓▓▓▓┃
┃▓▓ ▓▓▓ ▓▓      ▓    ▓▓▓    ▓▓▓▓▓┃    ┃ ▓▓▓▓                      ▓▓▓▓▓┃
┃▓ ▓▓▓   ▓▓  ▓▓ ▓ ▓ ▓ ▓ ▓▓▓   ▓ ▓┃    ┃▓▓▓▓▓                        ▓▓ ┃
┃▓▓▓ ▓ ▓   ▓▓▓     ▓   ▓      ▓  ┃    ┃▓▓▓▓▓     ▓▓▓                ▓▓ ┃
┃ ▓  ▓ ▓▓  ▓▓   ▓  ▓ ▓▓    ▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓  ▓▓▓               ▓▓  ┃
┃▓▓▓  ▓▓▓▓▓  ▓▓▓ ▓▓ ▓    ▓▓  ▓ ▓ ┃    ┃ ▓▓▓▓░▓▓▓     ▓▓▓▓▓      ▓▓▓▓▓  ┃
┃ ▓▓▓▓  ▓      ▓▓▓▓ ▓▓ ▓  ▓▓▓▓▓  ┃    ┃ ▓▓▓  ▓▓▓     ▓▓▓▓▓     ▓▓▓▓▓   ┃
┃  ▓   ▓▓▓ ▓ ▓ ▓ ▓ ▓  ▓  ▓▓▓▓    ┃    ┃      ▓▓▓     ░░░░░     ▓▓▓▓    ┃
┃   ▓▓▓ ▓▓   ▓▓ ▓ ▓     ▓▓▓▓▓    ┃    ┃      ▓▓▓     ░░░░░     ▓▓▓▓    ┃
┃▓   ▓  ▓▓▓▓ ▓ ▓ ▓ ▓▓▓   ▓    ▓  ┃    ┃   ▓▓▓▓▓▓  ▓▓▓▓▓░░░     ▓▓      ┃
┃▓ ▓▓▓▓  ▓  ▓▓ ▓ ▓▓ ▓  ▓ ▓▓▓  ▓▓▓┃    ┃▓▓▓▓▓░     ▓▓▓▓▓▓▓▓▓▓   ▓▓   ▓▓ ┃
┃▓▓  ▓      ▓▓ ▓  ▓ ▓▓   ▓▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓ ┃
┃▓▓ ▓ ▓▓▓▓▓  ▓▓▓▓▓ ▓ ▓ ▓ ▓▓▓▓▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓░░░░░░▓▓▓▓▓▓  ┃
┃▓▓▓▓ ▓▓ ▓▓▓   ▓  ▓   ▓ ▓ ▓      ┃    ┃▓▓▓▓▓▓▓▓▓▓  ░░░     ░░░░▓▓      ┃
┃  ▓▓ ▓▓    ▓▓ ▓  ▓▓ ▓   ▓▓    ▓▓┃    ┃  ▓▓▓▓▓▓▓▓   ░░        ░▓▓      ┃
┃  ▓▓▓▓▓▓▓▓  ▓▓  ▓   ▓▓ ▓▓  ▓▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓    ░         ▓▓      ┃
┃ ▓▓▓   ▓▓▓▓ ▓ ▓▓▓    ▓  ▓▓▓    ▓┃    ┃  ▓▓   ▓▓▓    ▓▓        ▓▓      ┃
┃   ▓ ▓  ▓  ▓  ▓▓  ▓▓ ▓ ▓▓ ▓ ▓▓  ┃    ┃              ▓▓        ▓▓      ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓   ▓  ▓▓  ▓▓ ▓▓▓▓▓▓  ▓ ▓▓▓ ▓ ┃    ┃                ▓▓▓▓       ▓▓   ┃
┃ ▓▓▓    ▓ ▓▓▓  ▓▓ ▓   ▓ ▓  ▓▓  ▓┃    ┃  ▓▓      ▓▓░░░▓▓▓▓▓       ▓▓   ┃
┃  ▓▓     ▓▓ ▓ ▓ ▓ ▓▓▓   ▓      ▓┃    ┃  ▓▓      ▓▓░░░▓▓▓▓▓            ┃
┃    ▓ ▓      ▓▓▓▓     ▓ ▓▓▓▓▓▓  ┃    ┃  ▓▓▓          ▓▓▓▓▓   ▓▓▓▓▓▓▓  ┃
┃ ▓▓▓ ▓▓▓▓ ▓     ▓ ▓ ▓ ▓▓  ▓▓ ▓  ┃    ┃  ▓▓▓▓▓▓▓      ▓▓▓▓▓░░▓▓▓▓▓▓▓▓  ┃
┃▓  ▓▓  ▓▓  ▓ ▓▓ ▓▓▓▓ ▓▓▓▓▓▓▓▓▓  ┃    ┃   ▓▓▓▓▓▓    ▓▓▓▓▓▓▓░░▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓▓ ▓▓▓   ▓▓▓ ▓ ▓▓    ▓▓▓   ▓┃    ┃    ▓▓▓▓▓    ▓▓▓▓▓▓▓░  ▓▓▓▓▓▓   ┃
┃    ▓▓  ▓   ▓   ▓  ▓  ▓ ▓▓▓ ▓▓  ┃    ┃    ▓▓▓▓▓      ▓▓  ░░  ▓▓▓▓▓▓   ┃
┃ ▓ ▓▓▓ ▓▓ ▓   ▓▓▓   ▓▓▓▓ ▓ ▓▓ ▓ ┃    ┃   ▓▓▓▓▓▓      ▓▓  ░▓▓▓▓▓▓▓▓▓   ┃
┃  ▓▓ ▓▓▓   ▓ ▓ ▓▓▓ ▓▓  ▓▓▓▓▓   ▓┃    ┃   ▓▓▓▓▓     ▓▓▓▓░░░▓▓▓▓▓▓▓▓    ┃
┃▓▓  ▓ ▓  ▓▓▓▓▓    ▓ ▓▓          ┃    ┃    ▓▓▓   ▓▓▓▓▓▓▓░░░▓▓          ┃
┃   ▓▓▓  ▓ ▓▓▓▓▓ ▓▓  ▓ ▓   ▓   ▓ ┃    ┃     ▓▓   ▓▓▓▓▓▓▓   ░░          ┃
┃▓▓   ▓▓    ▓ ▓▓ ▓ ▓  ▓ ▓ ▓▓   ▓ ┃    ┃     ▓▓    ▓▓▓▓▓▓   ░░          ┃
┃▓ ▓  ▓▓ ▓  ▓▓▓▓ ▓  ▓▓▓▓▓ ▓  ▓ ▓▓┃    ┃     ▓▓    ▓▓▓▓▓▓   ▓▓▓       ▓▓┃
┃ ▓▓ ▓ ▓ ▓ ▓▓ ▓ ▓     ▓   ▓ ▓  ▓▓┃    ┃ ▓▓░░░  ▓▓▓▓▓▓▓▓▓   ▓▓▓       ▓▓┃
┃ ▓▓▓ ▓  ▓▓▓▓  ▓ ▓▓ ▓▓▓▓ ▓    ▓▓ ┃    ┃ ▓▓░░░  ▓▓▓▓  ▓▓░   ▓▓▓         ┃
┃▓ ▓ ▓▓  ▓ ▓▓   ▓ ▓     ▓▓  ▓▓   ┃    ┃    ▓▓   ▓▓▓  ▓▓▓▓  ▓▓▓▓        ┃
┃   ▓▓▓▓  ▓▓ ▓▓▓▓▓▓▓▓ ▓▓  ▓▓▓ ▓  ┃    ┃    ▓▓▓  ▓▓▓▓▓▓▓▓▓░░▓▓▓▓        ┃
┃▓    ▓▓▓ ▓  ▓▓▓ ▓ ▓ ▓▓▓ ▓      ▓┃    ┃    ▓▓▓    ▓▓▓▓▓▓▓░░░▓▓▓▓       ┃
┃    ▓▓    ▓▓  ▓▓     ▓▓▓▓   ▓   ┃    ┃    ▓▓▓     ▓▓▓▓▓    ▓▓▓▓       ┃
┃▓▓▓ ▓ ▓▓    ▓▓▓ ▓▓ ▓    ▓▓ ▓▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓    ▓▓▓▓▓       ▓       ┃
┃▓ ▓▓ ▓▓▓▓ ▓ ▓▓ ▓  ▓▓▓▓  ▓   ▓ ▓ ┃    ┃▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓ ┃
┃▓▓  ▓     ▓ ▓  ▓▓  ▓▓▓  ▓▓  ▓▓▓▓┃    ┃▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓  ▓▓  ▓▓▓ ┃
┃ ▓ ▓   ▓    ▓ ▓▓▓▓▓  ▓▓ ▓▓  ▓ ▓ ┃    ┃  ░░        ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓ ┃
┃▓ ▓ ▓  ▓▓▓  ▓▓▓▓  ▓▓▓▓ ▓▓ ▓ ▓ ▓ ┃    ┃  ░░        ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃  ▓▓▓  ▓   ▓ ▓▓▓▓ ▓▓▓▓▓▓ ▓▓     ┃    ┃  ▓▓        ▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ┃
┃ ▓ ▓  ▓▓    ▓▓ ▓ ▓ ▓ ▓   ▓   ▓▓ ┃    ┃  ▓▓        ▓▓▓▓▓▓              ┃
┃▓ ▓▓   ▓▓▓ ▓   ▓▓ ▓       ▓  ▓ ▓┃    ┃  ▓▓   ░▓▓▓▓▓▓▓▓▓               ┃
┃  ▓ ▓▓   ▓  ▓▓▓▓ ▓ ▓        ▓▓  ┃    ┃ ▓▓▓▓▓   ▓▓▓▓▓▓▓            ▓▓  ┃
┃▓▓▓▓▓▓   ▓▓▓ ▓▓  ▓  ▓▓  ▓▓▓ ▓▓  ┃    ┃ ▓▓▓▓▓   ▓▓▓▓▓▓     ▓▓   ▓▓ ▓▓  ┃
┃▓   ▓ ▓▓  ▓▓ ▓▓ ▓ ▓ ▓▓▓▓ ▓▓     ┃    ┃    ▓▓ ░▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓     ┃
┃ ▓▓ ▓▓ ▓▓▓▓▓    ▓▓▓▓▓ ▓▓▓   ▓  ▓┃    ┃        ▓▓▓▓      ▓▓▓▓▓▓        ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓ ▓    ▓▓▓  ▓▓▓▓ ▓   ▓▓  ▓▓▓ ┃    ┃          ▓▓▓     ▓▓        ▓▓▓ ┃
┃ ▓   ▓    ▓▓▓ ▓   ▓▓▓ ▓ ▓  ▓▓▓▓▓┃    ┃          ▓▓▓     ▓▓▓       ▓▓▓▓┃
┃  ▓ ▓ ▓   ▓▓▓ ▓ ▓ ▓▓▓ ▓▓  ▓  ▓▓▓┃    ┃          ▓▓▓     ▓▓▓▓▓▓     ▓▓▓┃
┃ ▓    ▓▓ ▓▓▓▓        ▓ ▓  ▓  ▓▓▓┃    ┃          ▓▓▓         ▓▓     ▓▓▓┃
┃  ▓  ▓      ▓▓▓ ▓      ▓ ▓▓▓▓   ┃    ┃            ▓▓            ▓▓▓   ┃
┃▓  ▓   ▓ ▓▓ ▓▓  ▓ ▓   ▓ ▓ ▓ ▓ ▓ ┃    ┃            ▓▓            ▓▓▓   ┃
┃▓▓    ▓ ▓    ▓  ▓ ▓  ▓▓   ▓▓▓ ▓ ┃    ┃            ▓▓       ▓▓   ▓▓▓   ┃
┃   ▓  ▓ ▓▓▓▓▓ ▓   ▓▓ ▓▓   ▓▓  ▓▓┃    ┃       ▓▓▓▓▓▓▓    ▓▓▓▓▓   ▓▓▓▓▓▓┃
┃▓▓▓ ▓▓ ▓▓▓▓ ▓▓▓▓▓ ▓▓ ▓▓▓▓▓▓ ▓  ▓┃    ┃ ▓▓▓▓  ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓▓   ▓  ▓  ▓▓   ▓ ▓▓▓▓   ▓▓▓▓┃    ┃ ▓▓▓▓         ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓  ▓       ▓   ▓ ▓  ▓▓ ▓▓▓   ┃    ┃  ▓▓▓               ▓▓▓▓▓▓▓▓▓▓▓▓┃
┃▓ ▓ ▓▓  ▓▓▓▓     ▓▓ ▓ ▓▓▓ ▓  ▓▓▓┃    ┃  ▓▓▓▓   ▓▓▓           ▓▓▓░▓▓▓▓▓┃
┃▓ ▓▓▓▓▓   ▓▓▓▓  ▓   ▓   ▓▓ ▓ ▓▓▓┃    ┃  ▓▓▓▓   ▓▓▓▓▓             ▓▓▓▓▓┃
┃▓      ▓ ▓▓ ▓▓ ▓      ▓    ▓▓ ▓▓┃    ┃         ▓▓▓▓▓▓              ▓▓▓┃
┃   ▓▓    ▓ ▓▓ ▓ ▓▓ ▓▓▓▓  ▓ ▓  ▓ ┃    ┃          ▓▓▓▓▓▓▓▓  ▓▓          ┃
┃ ▓▓ ▓▓▓▓  ▓   ▓ ▓ ▓  ▓  ▓▓      ┃    ┃   ▓▓▓▓      ▓▓▓▓▓▓▓▓▓  ▓▓      ┃
┃  ▓  ▓▓ ▓▓  ▓▓▓▓▓▓▓ ▓▓  ▓  ▓▓  ▓┃    ┃   ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓  ▓▓      ┃
┃▓▓ ▓▓ ▓▓▓  ▓   ▓ ▓ ▓▓▓ ▓▓▓▓ ▓▓  ┃    ┃   ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ┃
┃▓  ▓▓    ▓   ▓▓  ▓       ▓▓ ▓   ┃    ┃   ▓▓         ▓▓▓▓      ▓▓▓▓▓   ┃
┃▓  ▓▓▓   ▓ ▓▓ ▓▓ ▓  ▓▓ ▓▓▓▓ ▓▓ ▓┃    ┃   ▓▓         ▓▓▓▓      ▓▓▓     ┃
┃      ▓▓▓▓▓  ▓  ▓▓     ▓ ▓▓ ▓  ▓┃    ┃       ▓▓▓    ▓▓▓▓      ▓▓▓     ┃
┃▓  ▓   ▓▓▓ ▓ ▓ ▓▓  ▓    ▓     ▓ ┃    ┃       ▓▓▓  ░░▓▓▓               ┃
┃▓▓ ▓▓▓   ▓ ▓▓ ▓▓   ▓ ▓▓       ▓▓┃    ┃   ▓▓▓       ░░░   ▓▓▓          ┃
┃   ▓▓▓  ▓  ▓ ▓ ▓ ▓ ▓▓ ▓▓ ▓▓ ▓▓▓ ┃    ┃   ▓▓▓        ░   ▓▓▓▓▓▓  ▓▓▓▓▓ ┃
┃▓  ▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓ ▓  ▓▓▓▓  ┃    ┃   ▓▓▓▓▓▓         ▓▓▓▓▓▓░░▓▓▓▓▓ ┃
┃ ▓ ▓▓  ▓▓▓   ▓▓    ▓▓  ▓▓▓ ▓ ▓▓ ┃    ┃  ▓▓▓▓▓▓▓         ▓▓▓▓▓▓░░▓▓▓▓▓ ┃
┃▓ ▓▓▓▓ ▓  ▓    ▓ ▓▓▓▓▓▓   ▓ ▓ ▓▓┃    ┃  ▓▓▓             ▓▓▓▓   ▓▓▓▓▓▓ ┃
┃▓ ▓ ▓    ▓ ▓▓▓ ▓   ▓     ▓▓ ▓▓  ┃    ┃  ▓▓▓         ▓▓   ▓▓▓   ▓▓▓▓▓▓ ┃
┃  ▓▓▓  ▓ ▓▓   ▓▓ ▓  ▓▓▓▓▓▓▓ ▓▓▓ ┃    ┃  ▓▓▓    ▓▓   ▓▓   ▓▓▓▓▓▓▓▓▓▓▓  ┃
┃▓        ▓▓ ▓ ▓▓ ▓▓▓▓ ▓ ▓ ▓  ▓  ┃    ┃         ▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃  ▓ ▓  ▓ ▓  ▓▓  ▓ ▓▓▓▓▓▓ ▓▓▓▓▓ ▓┃    ┃                ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓ ▓  ▓  ▓ ▓  ▓▓▓▓  ▓ ▓▓ ▓▓  ▓ ┃    ┃                 ▓▓   ▓▓▓▓▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓  ▓▓ ▓  ▓▓      ▓▓    ▓  ▓▓▓┃    ┃            ▓▓      ▓▓          ┃
┃ ▓  ▓▓ ▓    ▓▓  ▓▓ ▓▓▓▓ ▓▓▓ ▓ ▓ ┃    ┃    ▓▓      ▓▓      ▓▓ ▓▓▓▓▓    ┃
┃ ▓ ▓▓     ▓ ▓▓▓▓  ▓    ▓▓▓▓▓▓ ▓ ┃    ┃   ▓▓▓▓    ▓▓▓▓        ▓▓▓▓▓    ┃
┃▓   ▓▓▓▓  ▓▓ ▓▓  ▓   ▓ ▓▓ ▓▓    ┃    ┃   ▓▓▓▓▓  ▓▓▓▓▓▓▓▓     ▓▓▓▓▓    ┃
┃▓ ▓▓▓ ▓▓▓ ▓▓▓▓▓▓▓ ▓       ▓▓ ▓ ▓┃    ┃  ▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓       ▓▓    ┃
┃  ▓▓▓▓▓▓    ▓▓▓▓ ▓   ▓▓▓▓     ▓▓┃    ┃  ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓  ▓▓▓▓    ▓▓▓┃
┃ ▓    ▓▓▓▓▓    ▓▓ ▓ ▓▓▓▓▓▓▓ ▓▓▓ ┃    ┃  ▓   ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓▓┃
┃ ▓▓   ▓ ▓▓    ▓ ▓▓ ▓▓  ▓ ▓▓▓  ▓▓┃    ┃ ▓▓   ▓▓▓▓    ▓▓▓▓▓▓▓▓▓▓▓▓▓░░▓▓ ┃
┃▓▓▓▓ ▓▓▓   ▓  ▓▓▓▓▓▓▓ ▓▓ ▓  ▓▓▓ ┃    ┃▓▓▓  ▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓ ┃
┃▓  ▓ ▓▓  ▓   ▓   ▓▓▓▓ ▓▓ ▓      ┃    ┃▓▓   ▓▓▓       ▓▓▓▓▓▓▓▓▓▓▓      ┃
┃▓▓   ▓ ▓ ▓  ▓ ▓ ▓▓  ▓ ▓  ▓ ▓  ▓▓┃    ┃░░   ▓▓▓        ▓▓▓   ▓▓▓▓    ▓▓┃
┃  ▓▓ ▓ ▓    ▓   ▓ ▓   ▓▓▓▓▓ ▓▓▓▓┃    ┃░░   ▓▓▓              ▓▓▓▓░░░░▓▓┃
┃▓▓   ▓ ▓▓▓ ▓ ▓     ▓  ▓▓▓▓ ▓  ▓▓┃    ┃░░   ▓▓  ▓▓▓          ▓▓▓▓░░░░▓▓┃
┃▓ ▓▓ ▓   ▓▓   ▓   ▓ ▓▓ ▓    ▓  ▓┃    ┃▓▓▓      ▓▓▓▓       ▓▓▓▓  ░░░  ▓┃
┃▓▓▓  ▓ ▓  ▓▓▓▓▓  ▓▓▓ ▓▓  ▓▓▓▓  ▓┃    ┃▓▓▓       ▓▓▓▓▓     ▓▓▓   ▓▓▓  ▓┃
┃  ▓ ▓▓ ▓    ▓▓▓▓ ▓  ▓▓ ▓   ▓ ▓ ▓┃    ┃            ▓▓▓     ▓▓    ▓▓▓░▓▓┃
┃▓  ▓   ▓            ▓  ▓  ▓▓▓ ▓▓┃    ┃                          ▓▓▓▓▓▓┃
┃▓   ▓ ▓ ▓  ▓▓ ▓▓▓▓▓   ▓ ▓▓▓    ▓┃    ┃              ▓▓▓      ▓▓▓▓  ▓▓▓┃
┃▓▓▓ ▓ ▓▓▓▓    ▓▓▓   ▓  ▓▓▓  ▓▓ ▓┃    ┃▓▓▓▓   ▓▓     ▓▓▓      ▓▓▓   ▓▓▓┃
┃▓▓▓▓   ▓▓   ▓▓  ▓  ▓   ▓ ▓   ▓▓▓┃    ┃▓▓▓▓   ▓▓    ▓▓▓▓            ▓▓▓┃
┃  ▓▓      ▓  ▓▓ ▓    ▓      ▓ ▓▓┃    ┃ ▓▓▓        ▓▓▓▓▓            ▓▓▓┃
┃▓▓▓ ▓▓  ▓▓▓ ▓▓ ▓▓▓  ▓ ▓▓ ▓ ▓  ▓ ┃    ┃ ▓▓▓        ▓▓▓▓▓▓              ┃
┃ ▓    ▓    ▓▓  ▓▓▓▓▓     ▓▓ ▓  ▓┃    ┃ ▓▓▓        ░  ▓▓▓▓             ┃
┃  ▓▓▓    ▓▓ ▓  ▓▓▓▓   ▓▓        ┃    ┃ ▓▓▓▓      ░░  ▓▓▓▓             ┃
┃▓▓▓▓▓  ▓   ▓ ▓ ▓▓   ▓▓▓ ▓  ▓ ▓▓ ┃    ┃▓▓▓▓▓      ░░  ▓▓            ▓▓ ┃
┃▓ ▓ ▓ ▓▓▓▓ ▓      ▓▓     ▓   ▓▓▓┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓                ▓▓ ┃
┃▓▓▓▓  ▓▓▓ ▓▓▓ ▓▓ ▓▓  ▓▓▓▓▓▓ ▓▓ ▓┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓  ▓▓▓   ▓▓▓▓▓▓▓▓▓ ┃
┃ ▓▓▓    ▓▓  ▓▓  ▓▓▓ ▓ ▓▓  ▓▓▓   ┃    ┃ ▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓▓▓▓ ┃
┃ ▓ ▓▓ ▓▓▓▓▓▓▓▓ ▓▓ ▓▓  ▓ ▓▓   ▓▓ ┃    ┃ ▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓░░░▓▓▓▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓  ▓▓▓   ▓▓  ▓▓┃    ┃▓▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓       ░░▓▓▓▓ ┃
┃▓▓▓▓     ▓▓▓▓  ▓▓      ▓ ▓ ▓▓▓  ┃    ┃▓▓▓▓    ▓▓▓▓▓  ▓▓▓        ░▓▓▓▓ ┃
┃ ▓ ▓▓   ▓▓  ▓  ▓▓▓▓▓   ▓▓ ▓ ▓▓▓ ┃    ┃  ▓▓           ▓▓▓         ▓▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓  ▓▓▓▓  ▓▓▓ ▓  ▓  ▓ ▓▓ ▓ ▓ ┃    ┃        ▓▓▓  ▓▓                 ┃
┃▓  ▓ ▓  ▓ ▓  ▓ ▓ ▓ ▓    ▓ ▓▓ ▓ ▓┃    ┃       ▓▓▓▓  ▓▓                 ┃
┃▓ ▓  ▓▓▓▓ ▓ ▓▓   ▓ ▓  ▓ ▓ ▓ ▓▓▓▓┃    ┃▓▓     ▓▓    ▓▓  ▓▓▓        ▓▓▓▓┃
┃▓▓     ▓      ▓▓▓▓▓▓▓ ▓   ▓  ▓▓▓┃    ┃▓▓     ▓▓    ▓▓▓▓▓▓▓▓       ▓▓▓▓┃
┃▓▓  ▓ ▓ ▓▓▓  ▓▓▓▓  ▓▓       ▓▓▓ ┃    ┃▓▓     ▓▓▓▓   ▓▓▓▓▓▓▓       ▓▓▓ ┃
┃▓▓  ▓   ▓▓▓ ▓  ▓ ▓ ▓▓ ▓▓   ▓▓▓  ┃    ┃▓▓     ▓▓▓▓   ▓▓▓▓▓▓▓       ▓▓▓ ┃
┃▓ ▓▓ ▓ ▓▓  ▓▓ ▓ ▓▓▓▓ ▓ ▓ ▓  ▓▓▓▓┃    ┃▓▓▓▓▓  ▓▓      ▓▓▓▓▓▓       ▓▓▓ ┃
┃ ▓▓▓▓  ▓▓    ▓  ▓▓ ▓▓ ▓▓ ▓▓   ▓ ┃    ┃▓▓▓▓▓  ▓▓       ▓▓▓▓▓░░▓▓▓▓     ┃
┃▓▓ ▓▓      ▓  ▓▓ ▓▓▓ ▓  ▓▓▓   ▓ ┃    ┃▓▓▓▓▓           ▓▓▓▓▓░░▓▓▓▓     ┃
┃▓ ▓ ▓ ▓▓ ▓  ▓   ▓▓▓▓  ▓ ▓  ▓▓  ▓┃    ┃  ▓▓▓            ▓▓▓▓░░░        ┃
┃    ▓ ▓  ▓▓   ▓   ▓▓▓ ▓▓ ▓  ▓▓ ▓┃    ┃                 ▓▓▓▓░░     ▓▓  ┃
┃    ▓▓ ▓ ▓   ▓  ▓▓▓▓▓  ▓    ▓ ▓▓┃    ┃      ░         ▓▓▓▓▓       ▓▓  ┃
┃ ▓    ▓▓▓  ▓ ▓▓ ▓▓▓ ▓ ▓ ▓ ▓▓▓▓  ┃    ┃     ▓▓▓▓       ▓▓▓▓      ▓▓▓▓  ┃
┃▓▓ ▓ ▓ ▓▓      ▓ ▓        ▓▓ ▓▓ ┃    ┃     ▓▓▓▓       ░░░       ▓▓▓▓  ┃
┃  ▓   ▓▓▓▓ ▓ ▓  ▓ ▓  ▓    ▓▓   ▓┃    ┃     ▓▓▓▓▓▓    ░░░░       ▓▓    ┃
┃ ▓  ▓▓▓  ▓▓▓ ▓▓▓  ▓▓▓▓   ▓ ▓  ▓▓┃    ┃     ▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓         ▓▓┃
┃  ▓▓ ▓ ▓▓▓ ▓▓ ▓▓   ▓  ▓▓     ▓▓ ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓       ▓▓▓┃
┃   ▓ ▓▓▓ ▓ ▓ ▓ ▓ ▓▓▓ ▓ ▓ ▓▓▓ ▓ ▓┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓     ▓▓ ┃
┃ ▓▓▓  ▓  ▓▓      ▓  ▓▓▓▓   ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓        ┃
┃ ▓▓▓ ▓▓▓▓ ▓      ▓▓▓ ▓ ▓▓▓ ▓    ┃    ┃ ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓        ┃
┃▓▓▓▓▓  ▓ ▓▓▓▓▓▓ ▓▓▓ ▓▓▓     ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓        ┃
┃▓ ▓▓ ▓▓    ▓         ▓▓▓▓  ▓   ▓┃    ┃ ▓▓▓               ▓▓▓▓▓        ┃
┃ ▓ ▓       ▓     ▓▓ ▓  ▓ ▓▓▓▓ ▓▓┃    ┃                   ▓▓▓▓▓▓▓▓▓▓▓▓ ┃
┃  ▓  ▓▓▓▓    ▓▓▓▓  ▓▓▓▓▓▓▓  ▓▓ ▓┃    ┃      ▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓   ▓     ▓▓  ▓▓ ▓▓    ▓ ▓ ▓▓▓┃    ┃     ▓▓▓     ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓┃
┃ ▓ ▓▓▓▓▓  ▓▓ ▓ ▓▓▓▓▓ ▓  ▓▓▓     ┃    ┃  ▓▓▓▓▓▓        ▓▓▓▓▓▓  ▓▓      ┃
┃ ▓▓▓   ▓▓    ▓    ▓ ▓ ▓▓▓   ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓       ▓▓▓▓▓   ▓▓      ┃
┃ ▓ ▓▓ ▓▓▓ ▓  ▓  ▓▓▓ ▓▓   ▓    ▓▓┃    ┃ ▓▓▓▓▓▓▓▓       ▓▓▓▓▓   ░       ┃
┃▓▓▓▓▓ ▓       ▓▓▓▓▓▓    ▓   ▓▓  ┃    ┃ ▓▓▓▓           ▓▓▓▓            ┃
┃▓  ▓  ▓  ▓▓ ▓▓    ▓ ▓    ▓▓▓  ▓ ┃    ┃  ▓▓▓    ▓▓▓▓                   ┃
┃ ▓ ▓ ▓  ▓▓▓▓▓ ▓        ▓▓   ▓ ▓▓┃    ┃         ▓▓▓▓          ▓▓    ▓▓▓┃
┃  ▓▓▓ ▓▓     ▓  ▓    ▓▓▓▓  ▓▓▓▓▓┃    ┃                       ▓▓    ▓▓▓┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃  ▓▓▓  ▓  ▓ ▓▓▓▓▓▓ ▓▓▓ ▓ ▓▓▓  ▓ ┃    ┃   ▓▓      ▓▓▓▓▓    ▓▓▓   ▓▓    ┃
┃ ▓ ▓▓  ▓   ▓▓▓▓ ▓  ▓ ▓▓   ▓▓▓▓  ┃    ┃  ▓▓▓      ▓▓▓▓▓    ▓▓▓   ▓▓    ┃
┃ ▓ ▓  ▓▓ ▓ ▓▓         ▓ ▓ ▓▓  ▓▓┃    ┃  ▓▓▓      ▓▓             ▓▓    ┃
┃▓ ▓▓▓  ▓   ▓▓   ▓▓ ▓▓      ▓    ┃    ┃  ▓▓▓      ▓▓   ▓▓              ┃
┃▓▓  ▓▓ ▓▓▓ ▓ ▓▓ ▓▓  ▓▓▓     ▓ ▓ ┃    ┃▓▓▓▓▓  ▓▓▓▓▓▓▓▓ ▓▓  ▓▓▓         ┃
┃▓▓ ▓  ▓  ▓ ▓▓▓▓ ▓    ▓▓  ▓    ▓ ┃    ┃▓▓     ▓▓▓▓▓▓▓▓     ▓▓▓         ┃
┃▓  ▓   ▓▓▓▓ ▓▓▓  ▓ ▓▓ ▓▓    ▓▓▓▓┃    ┃▓▓     ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓     ▓▓ ┃
┃▓▓   ▓▓ ▓     ▓▓ ▓▓▓   ▓▓ ▓ ▓ ▓ ┃    ┃▓▓     ▓▓▓    ░░░▓▓▓▓▓▓▓▓    ▓▓ ┃
┃ ▓▓  ▓ ▓▓▓    ▓ ▓▓▓ ▓▓▓▓▓ ▓▓ ▓▓▓┃    ┃▓▓     ▓▓▓     ░░▓▓▓▓▓▓▓▓▓▓▓    ┃
┃▓   ▓ ▓▓ ▓▓ ▓ ▓▓  ▓▓    ▓▓▓▓▓ ▓ ┃    ┃       ▓▓▓        ▓▓    ▓▓▓▓    ┃
┃  ▓▓▓  ▓▓▓  ▓ ▓   ▓▓ ▓▓ ▓       ┃    ┃  ▓▓▓  ▓▓▓        ▓▓    ░░      ┃
┃▓▓▓▓ ▓  ▓▓  ▓ ▓  ▓    ▓ ▓ ▓▓ ▓  ┃    ┃▓▓▓▓▓   ▓▓           ▓▓░░░      ┃
┃▓▓▓  ▓    ▓ ▓    ▓▓ ▓▓▓  ▓  ▓▓▓▓┃    ┃▓▓▓▓▓                ▓▓░░▓▓▓▓▓▓ ┃
┃▓ ▓▓▓▓▓ ▓ ▓   ▓▓ ▓  ▓ ▓▓▓ ▓ ▓▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓            ▓▓░░▓▓▓▓▓▓ ┃
┃ ▓ ▓ ▓▓▓▓▓  ▓▓     ▓ ▓▓  ▓▓▓▓▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓               ▓▓▓▓▓▓ ┃
┃▓▓▓▓ ▓ ▓  ▓▓  ▓  ▓▓ ▓    ▓▓   ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓     ▓▓▓▓▓▓ ┃
┃  ▓▓ ▓ ▓▓▓ ▓▓▓▓▓ ▓▓▓ ▓ ▓▓▓ ▓▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓ ┃
┃ ▓  ▓ ▓▓ ▓▓ ▓  ▓▓▓ ▓       ▓  ▓▓┃    ┃    ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓      ▓▓  ▓▓┃
┃ ▓  ▓      ▓▓▓  ▓  ▓▓  ▓ ▓ ▓  ▓▓┃    ┃    ▓▓    ▓▓▓▓▓▓▓         ▓▓  ▓▓┃
┃▓   ▓ ▓  ▓ ▓ ▓▓▓          ▓▓▓   ┃    ┃    ▓▓    ▓▓▓▓▓▓▓         ▓▓▓   ┃
┃▓  ▓▓▓   ▓▓▓▓▓ ▓▓▓ ▓▓▓ ▓▓▓ ▓▓▓ ▓┃    ┃   ▓▓▓▓   ▓▓▓▓▓▓▓     ░▓▓▓▓▓▓   ┃
┃▓  ▓▓▓▓▓▓  ▓  ▓   ▓ ▓ ▓▓▓ ▓   ▓ ┃    ┃   ▓▓▓▓▓▓▓▓▓▓▓       ░░▓▓▓▓▓▓▓  ┃
┃▓▓▓▓▓ ▓▓ ▓ ▓▓▓    ▓▓   ▓  ▓▓▓▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓    ▓▓▓▓▓▓▓ ┃
┃ ▓▓  ▓▓▓▓ ▓ ▓   ▓▓ ▓▓   ▓▓  ▓  ▓┃    ┃▓▓▓   ▓▓▓▓▓▓░░    ▓▓         ▓▓ ┃
┃▓       ▓▓ ▓ ▓ ▓ ▓    ▓ ▓ ▓  ▓▓ ┃    ┃      ▓▓▓▓▓▓▓░░              ▓▓ ┃
┃▓ ▓▓ ▓▓▓▓ ▓▓▓ ▓ ▓ ▓▓ ▓ ▓  ▓   ▓ ┃    ┃  ▓▓ ▓▓▓▓▓▓▓▓░░░             ▓▓ ┃
┃  ▓▓ ▓  ▓ ▓▓▓   ▓   ▓▓ ▓ ▓   ▓▓ ┃    ┃  ▓▓ ▓  ▓▓▓▓▓   ▓▓▓▓▓        ▓▓ ┃
┃ ▓   ▓   ▓   ▓  ▓▓▓▓▓   ▓  ▓ ▓▓ ┃    ┃     ▓  ▓▓      ▓▓▓▓▓        ▓▓ ┃
┃▓ ▓ ▓▓  ▓▓  ▓  ▓ ▓▓▓▓ ▓▓▓▓▓  ▓▓▓┃    ┃    ▓▓  ▓▓      ▓▓▓▓▓        ▓▓▓┃
┃▓▓  ▓▓▓ ▓▓▓ ▓   ▓  ▓▓  ▓  ▓ ▓▓ ▓┃    ┃    ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓    ▓▓▓▓┃
┃▓  ▓▓ ▓▓ ▓▓▓▓ ▓▓▓   ▓▓▓     ▓▓ ▓┃    ┃    ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓    ▓▓▓ ┃
┃▓▓   ▓▓▓   ▓       ▓▓ ▓▓▓ ▓▓▓▓ ▓┃    ┃      ▓▓            ▓▓▓▓    ▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓▓  ▓▓ ▓▓  ▓▓▓▓ ▓ ▓ ▓   ▓▓   ▓┃    ┃      ▓▓▓▓▓                     ┃
┃▓ ▓ ▓▓▓▓▓▓▓ ▓ ▓ ▓       ▓  ▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓▓                     ┃
┃▓▓▓▓ ▓▓▓ ▓ ▓      ▓ ▓ ▓    ▓ ▓▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓                  ▓▓▓ ┃
┃▓▓ ▓▓▓  ▓     ▓  ▓  ▓ ▓ ▓▓ ▓ ▓▓ ┃    ┃▓▓▓▓▓▓▓▓▓▓          ▓▓▓▓    ▓▓▓▓┃
┃    ▓▓▓ ▓▓ ▓▓ ▓  ▓ ▓▓▓ ▓▓   ▓▓▓▓┃    ┃    ▓▓  ▓▓   ▓▓     ▓▓▓▓▓▓  ▓▓▓▓┃
┃▓▓▓  ▓  ▓▓   ▓▓ ▓  ▓ ▓▓ ▓▓▓ ▓ ▓▓┃    ┃ ▓▓     ▓▓  ▓▓▓     ▓▓▓▓▓▓  ▓▓▓▓┃
┃ ▓▓  ▓      ▓▓▓     ▓▓▓ ▓   ▓  ▓┃    ┃ ▓▓         ▓▓▓     ▓▓▓▓▓       ┃
┃ ▓      ▓▓ ▓▓▓▓▓ ▓▓▓  ▓ ▓ ▓▓    ┃    ┃            ▓▓▓  ▓▓             ┃
┃▓     ▓         ▓▓      ▓ ▓ ▓▓▓ ┃    ┃                ▓▓▓        ▓▓▓▓ ┃
┃  ▓  ▓▓ ▓▓ ▓▓▓   ▓▓▓  ▓ ▓  ▓▓ ▓▓┃    ┃       ▓▓       ▓▓▓        ▓▓▓▓ ┃
┃▓▓     ▓▓     ▓▓▓    ▓▓▓    ▓▓ ▓┃    ┃       ▓▓     ▓▓▓▓▓  ▓▓▓   ▓▓▓  ┃
┃   ▓▓  ▓   ▓▓ ▓▓▓▓▓▓▓▓▓▓   ▓▓ ▓ ┃    ┃              ▓▓▓▓▓▓▓▓▓▓   ▓▓▓  ┃
┃ ▓ ▓ ▓▓  ▓▓▓  ▓▓ ▓▓▓▓ ▓ ▓▓ ▓▓▓  ┃    ┃   ▓▓▓   ▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃   ▓ ▓   ▓  ▓▓ ▓▓▓ ▓ ▓ ▓▓▓ ▓▓   ┃    ┃   ▓▓▓   ▓▓▓░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓▓ ▓▓ ▓▓▓▓ ▓  ▓▓▓ ▓▓   ▓▓ ▓▓▓▓┃    ┃   ▓▓▓ ▓▓▓▓▓   ▓▓▓▓▓    ▓▓▓▓▓▓▓▓┃
┃▓   ▓  ▓  ▓ ▓  ▓▓▓▓    ▓▓▓▓    ▓┃    ┃       ▓▓▓▓    ▓▓▓▓     ▓▓▓   ▓▓┃
┃  ▓  ▓ ▓▓▓  ▓ ▓▓▓▓▓   ▓    ▓ ▓▓▓┃    ┃      ▓▓▓▓     ▓▓▓▓           ▓▓┃
┃ ▓▓▓  ▓ ▓▓    ▓   ▓▓ ▓▓  ▓      ┃    ┃     ▓▓▓▓▓           ▓▓         ┃
┃▓▓  ▓▓▓▓  ▓  ▓ ▓  ▓  ▓▓▓▓   ▓▓▓▓┃    ┃▓▓  ▓▓▓▓▓▓           ▓▓         ┃
┃▓▓  ▓▓▓▓▓▓ ▓▓▓▓     ▓     ▓▓   ▓┃    ┃▓▓  ▓▓▓▓▓▓                      ┃
┃▓ ▓▓▓ ▓ ▓▓  ▓ ▓    ▓▓   ▓▓   ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓         ▓▓           ┃
┃  ▓     ▓▓   ▓   ▓▓▓ ▓▓▓▓     ▓▓┃    ┃      ▓▓▓▓         ▓▓▓▓         ┃
┃▓ ▓   ▓▓▓  ▓  ▓▓     ▓ ▓  ▓  ▓ ▓┃    ┃      ▓▓▓▓          ▓▓▓         ┃
┃▓   ▓▓▓ ▓▓     ▓   ▓ ▓   ▓ ▓ ▓  ┃    ┃    ▓▓▓▓▓     ▓▓    ░░          ┃
┃▓ ▓▓▓▓ ▓    ▓▓▓▓  ▓ ▓  ▓ ▓▓▓  ▓ ┃    ┃    ▓▓▓     ▓▓▓▓     ░    ▓▓▓   ┃
┃ ▓        ▓▓▓▓▓ ▓▓▓  ▓▓▓▓ ▓ ▓▓▓ ┃    ┃           ▓▓▓▓▓▓▓   ▓▓▓░░▓▓▓▓  ┃
┃   ▓▓▓  ▓  ▓▓▓▓▓▓   ▓▓ ▓ ▓ ▓▓  ▓┃    ┃   ▓▓▓     ▓▓▓▓▓▓▓   ▓▓▓░░▓▓▓▓  ┃
┃▓▓▓▓ ▓▓▓  ▓ ▓▓   ▓    ▓▓   ▓ ▓  ┃    ┃   ▓▓▓     ▓▓▓▓▓▓▓   ▓▓    ▓▓▓  ┃
┃     ▓  ▓▓   ▓▓ ▓ ▓ ▓▓ ▓    ▓▓  ┃    ┃             ▓▓▓▓▓         ▓▓▓  ┃
┃ ▓▓▓ ▓ ▓▓  ▓  ▓▓▓ ▓  ▓   ▓▓▓▓▓  ┃    ┃              ▓▓▓▓        ▓▓▓▓  ┃
┃▓  ▓    ▓     ▓  ▓▓    ▓▓ ▓     ┃    ┃              ▓▓▓▓        ▓▓    ┃
┃  ▓  ▓▓▓   ▓ ▓▓▓▓ ▓  ▓▓   ▓▓▓ ▓ ┃    ┃              ▓▓▓         ▓▓    ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃   ▓▓▓▓▓▓  ▓▓▓  ▓▓       ▓▓   ▓▓┃    ┃   ▓▓▓▓                         ┃
┃▓ ▓▓▓▓▓  ▓     ▓▓ ▓▓▓▓▓▓   ▓ ▓  ┃    ┃   ▓▓▓▓        ▓▓░░░▓▓▓         ┃
┃    ▓ ▓ ▓  ▓▓  ▓   ▓ ▓▓ ▓▓▓▓▓  ▓┃    ┃   ▓▓▓▓        ▓▓░░░▓▓▓   ▓▓    ┃
┃▓▓ ▓▓▓▓▓    ▓  ▓▓▓▓       ▓▓    ┃    ┃   ▓▓▓▓        ▓▓░░░      ▓▓    ┃
┃ ▓ ▓▓ ▓ ▓    ▓ ▓▓  ▓ ▓▓   ▓▓ ▓▓▓┃    ┃▓▓ ▓▓▓▓░      ▓▓▓░░       ▓▓▓   ┃
┃▓▓ ▓▓▓▓ ▓ ▓▓  ▓▓  ▓ ▓  ▓▓▓▓ ▓▓  ┃    ┃▓▓ ▓▓▓▓░░     ▓▓▓░        ▓▓▓   ┃
┃▓   ▓▓  ▓ ▓  ▓▓▓▓▓ ▓ ▓  ▓       ┃    ┃   ▓▓▓▓░  ▓▓▓▓▓▓▓░              ┃
┃▓ ▓▓ ▓▓  ▓▓▓▓ ▓ ▓ ▓    ▓  ▓▓▓   ┃    ┃    ▓▓    ▓▓▓▓▓▓░░              ┃
┃    ▓▓  ▓  ▓▓  ▓     ▓▓ ▓▓ ▓ ▓ ▓┃    ┃    ▓▓     ▓▓▓▓▓▓░       ▓▓▓    ┃
┃▓   ▓▓ ▓▓   ▓▓▓ ▓▓ ▓  ▓▓  ▓▓▓  ▓┃    ┃    ▓▓      ▓▓▓▓▓▓   ▓▓░▓▓▓▓▓   ┃
┃  ▓   ▓      ▓▓▓▓▓ ▓▓▓▓ ▓▓▓▓ ▓▓ ┃    ┃            ▓▓▓▓▓▓ ▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃  ▓▓▓ ▓▓  ▓ ▓  ▓▓▓  ▓▓    ▓  ▓▓▓┃    ┃  ▓▓  ░       ▓▓▓▓ ▓▓▓  ▓▓▓  ▓▓▓┃
┃▓▓▓ ▓ ▓ ▓▓▓▓  ▓    ▓▓  ▓▓▓▓    ▓┃    ┃▓▓▓▓░▓▓▓▓▓▓▓       ▓▓▓  ▓▓▓     ┃
┃▓▓ ▓  ▓ ▓ ▓▓  ▓   ▓ ▓▓▓ ▓▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓   ┃
┃  ▓ ▓ ▓▓▓▓ ▓ ▓▓▓▓▓▓▓▓ ▓ ▓▓▓▓▓   ┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ┃
┃▓ ▓ ▓▓  ▓▓  ▓ ▓▓▓  ▓      ▓ ▓ ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓┃
┃ ▓▓▓  ▓▓ ▓▓▓ ▓      ▓  ▓▓▓  ▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓              ▓▓┃
┃▓▓  ▓▓▓▓ ▓ ▓▓▓▓ ▓▓▓   ▓▓  ▓  ▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                ┃
┃▓▓▓▓  ▓▓▓▓▓ ▓▓▓▓  ▓▓  ▓  ▓      ┃    ┃▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓       ▓▓       ┃
┃ ▓ ▓  ▓    ▓ ▓▓▓   ▓   ▓▓▓    ▓▓┃    ┃      ▓▓▓   ▓▓▓▓       ▓▓▓    ▓▓┃
┃    ▓▓▓ ▓▓  ▓▓ ▓▓   ▓  ▓ ▓  ▓▓▓▓┃    ┃       ░░    ▓▓▓       ▓▓▓   ▓▓▓┃
┃  ▓    ▓ ▓   ▓   ▓  ▓▓▓▓ ▓    ▓▓┃    ┃       ░░    ▓▓▓    ▓▓▓▓▓▓   ▓▓▓┃
┃▓▓▓▓▓▓ ▓▓  ▓ ▓▓▓▓▓▓ ▓▓▓ ▓ ▓▓▓▓▓▓┃    ┃ ▓▓▓   ▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓┃
┃▓ ▓ ▓  ▓▓▓   ▓▓  ▓▓▓▓▓▓▓▓  ▓ ▓ ▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓┃
┃ ▓▓▓ ▓ ▓▓▓▓  ▓ ▓  ▓▓  ▓▓    ▓ ▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓     ░░░┃
┃  ▓▓ ▓▓▓▓   ▓▓  ▓▓▓  ▓▓   ▓▓ ▓  ┃    ┃ ▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓          ░░░┃
┃▓▓ ▓▓ ▓  ▓  ▓▓ ▓ ▓  ▓     ▓   ▓▓┃    ┃ ▓▓▓▓▓▓     ▓▓▓▓▓▓▓          ▓▓▓┃
┃ ▓▓▓ ▓▓  ▓▓▓ ▓▓▓ ▓▓▓ ▓ ▓     ▓▓▓┃    ┃ ▓▓▓▓▓▓     ▓▓▓▓▓▓▓          ▓▓▓┃
┃ ▓  ▓▓▓▓  ▓ ▓▓  ▓ ▓ ▓  ▓    ▓▓  ┃    ┃     ▓▓                      ░  ┃
┃      ▓ ▓▓ ▓ ▓  ▓  ▓▓    ▓▓▓▓  ▓┃    ┃     ▓▓▓▓▓                      ┃
┃▓▓▓▓ ▓▓ ▓▓      ▓  ▓ ▓▓ ▓  ▓    ┃    ┃▓▓▓▓▓▓▓▓▓▓                      ┃
┃▓▓ ▓▓▓▓▓▓ ▓▓     ▓▓   ▓    ▓ ▓  ┃    ┃▓▓▓▓▓▓▓▓▓▓                      ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓▓▓▓▓ ▓  ▓▓▓▓ ▓   ▓  ▓  ▓   ▓▓ ▓┃    ┃         ▓▓▓▓               ▓▓  ┃
┃▓   ▓ ▓ ▓▓ ▓▓   ▓▓▓    ▓▓  ▓▓▓  ┃    ┃         ▓▓▓▓   ▓▓▓        ▓▓▓  ┃
┃ ▓  ▓   ▓ ▓ ▓  ▓▓ ▓▓  ▓▓   ▓▓  ▓┃    ┃         ░░     ▓▓▓        ▓▓▓  ┃
┃   ▓   ▓  ▓   ▓   ▓  ▓ ▓     ▓▓ ┃    ┃         ░░       ▓▓        ▓▓  ┃
┃▓▓▓▓    ▓ ▓   ▓ ▓ ▓▓▓ ▓ ▓  ▓▓   ┃    ┃▓▓▓▓     ░░   ▓▓  ▓▓▓       ▓▓  ┃
┃▓▓▓ ▓▓▓▓▓▓ ▓▓ ▓▓▓ ▓▓▓   ▓   ▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓   ▓▓  ▓▓▓       ▓▓▓ ┃
┃▓ ▓ ▓▓▓  ▓▓   ▓ ▓  ▓ ▓ ▓ ▓ ▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓  ▓▓        ▓▓       ▓▓▓ ┃
┃ ▓ ▓  ▓  ▓ ▓       ▓  ▓      ▓ ▓┃    ┃ ▓▓   ▓  ▓▓▓                    ┃
┃ ▓▓   ▓▓ ▓▓▓▓▓ ▓ ▓  ▓ ▓   ▓     ┃    ┃ ▓▓   ▓  ▓▓▓▓                   ┃
┃▓▓▓  ▓    ▓ ▓  ▓▓ ▓  ▓ ▓   ▓▓   ┃    ┃ ▓▓   ▓   ▓▓▓▓ ▓▓▓        ▓▓    ┃
┃ ▓▓▓▓▓▓ ▓ ▓▓▓▓▓ ▓▓▓▓▓▓ ▓ ▓▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓  ▓▓▓▓ ▓▓▓       ▓▓▓▓▓▓ ┃
┃  ▓   ▓▓▓ ▓▓      ▓  ▓  ▓▓▓▓ ▓▓ ┃    ┃      ▓▓▓▓▓▓▓            ▓▓▓▓▓▓ ┃
┃   ▓  ▓▓ ▓  ▓   ▓  ▓  ▓   ▓ ▓ ▓▓┃    ┃      ▓▓▓▓▓▓▓              ▓▓▓▓ ┃
┃  ▓ ▓▓▓  ▓▓▓  ▓  ▓▓        ▓▓▓  ┃    ┃          ▓▓▓    ▓▓        ▓▓   ┃
┃ ▓    ▓   ▓ ▓▓▓  ▓▓ ▓▓ ▓   ▓    ┃    ┃          ▓▓▓▓▓  ▓▓▓       ▓▓   ┃
┃          ▓ ▓▓▓▓▓▓ ▓ ▓    ▓▓▓  ▓┃    ┃          ▓▓▓▓▓▓▓▓▓▓▓           ┃
┃▓ ▓▓   ▓▓▓▓▓   ▓▓▓ ▓ ▓ ▓   ▓    ┃    ┃          ▓▓   ▓▓▓▓▓▓▓▓         ┃
┃   ▓ ▓  ▓ ▓  ▓ ▓ ▓▓▓ ▓▓▓  ▓ ▓▓ ▓┃    ┃  ▓▓▓           ▓▓▓▓▓▓▓▓        ┃
┃▓▓▓▓▓▓▓    ▓▓▓  ▓   ▓▓ ▓   ▓▓ ▓ ┃    ┃  ▓▓▓▓▓         ▓▓  ▓▓▓▓        ┃
┃ ▓ ▓  ▓▓  ▓▓  ▓ ▓▓  ▓▓ ▓    ▓  ▓┃    ┃  ▓▓▓▓▓         ▓▓  ▓▓▓         ┃
┃    ▓▓▓        ▓▓ ▓ ▓ ▓      ▓  ┃    ┃  ▓▓▓▓▓        ▓▓▓▓▓▓▓▓         ┃
┃▓▓▓▓▓▓▓   ▓ ▓ ▓  ▓▓▓▓▓  ▓ ▓ ▓▓ ▓┃    ┃▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓    ▓▓   ┃
┃▓▓ ▓▓▓▓▓ ▓▓ ▓▓ ▓▓▓▓▓  ▓▓ ▓▓▓▓   ┃    ┃▓▓▓▓▓▓▓  ▓▓   ▓▓▓▓▓▓▓▓▓▓▓░░▓▓   ┃
┃▓▓▓▓ ▓   ▓ ▓   ▓▓  ▓▓ ▓▓▓ ▓    ▓┃    ┃▓▓▓▓▓▓▓  ▓▓  ▓▓▓▓  ▓▓▓▓▓▓░░░    ┃
┃▓▓▓ ▓▓ ▓ ▓▓  ▓▓ ▓  ▓  ▓▓▓  ▓   ▓┃    ┃▓▓▓▓▓▓▓▓▓▓   ▓▓▓   ▓▓▓▓▓▓░░░    ┃
┃▓ ▓▓ ▓▓▓▓▓   ▓▓  ▓▓ ▓▓▓ ▓ ▓▓▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓   ▓▓   ▓▓▓▓▓▓  ▓▓▓▓▓▓┃
┃ ▓ ▓     ▓ ▓  ▓   ▓▓▓     ▓   ▓▓┃    ┃ ▓▓▓▓   ▓▓▓  ▓▓   ▓▓▓     ▓  ▓▓▓┃
┃ ▓▓▓▓  ▓ ▓▓▓▓ ▓▓ ▓ ▓▓  ▓▓▓▓  ▓▓▓┃    ┃ ▓▓▓▓   ▓▓▓  ▓▓   ▓▓▓  ▓▓▓▓   ▓▓┃
┃▓▓  ▓▓▓ ▓  ▓ ▓     ▓▓▓ ▓ ▓ ▓    ┃    ┃ ▓▓▓▓▓▓▓▓    ▓▓   ▓▓▓░░▓▓▓▓     ┃
┃  ▓ ▓ ▓▓  ▓  ▓▓▓▓▓▓▓ ▓ ▓  ▓▓ ▓▓ ┃    ┃     ▓▓▓▓     ▓▓▓▓▓▓▓░░▓▓▓▓     ┃
┃  ▓    ▓▓▓▓  ▓ ▓ ▓    ▓ ▓▓ ▓   ▓┃    ┃      ▓▓▓▓▓    ▓▓▓▓    ▓▓▓      ┃
┃   ▓ ▓▓  ▓▓ ▓    ▓▓  ▓ ▓▓▓▓ ▓▓▓ ┃    ┃         ▓▓             ▓▓      ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓▓  ▓▓▓▓▓▓ ▓ ▓  ▓▓    ▓  ▓▓ ▓ ┃    ┃ ▓▓▓    ▓▓▓▓▓▓                  ┃
┃ ▓▓▓ ▓  ▓ ▓▓▓ ▓▓  ▓ ▓ ▓▓ ▓      ┃    ┃▓▓▓▓    ▓▓▓▓▓▓▓                 ┃
┃▓▓▓   ▓  ▓▓ ▓▓ ▓▓  ▓▓ ▓ ▓ ▓ ▓ ▓ ┃    ┃▓▓▓▓░░░▓▓▓▓▓▓▓▓▓▓        ░      ┃
┃▓ ▓▓▓▓ ▓▓▓   ▓ ▓▓▓▓  ▓  ▓ ▓▓ ▓  ┃    ┃▓▓▓▓░░░▓▓▓▓  ▓▓▓▓░      ░░░     ┃
┃▓ ▓    ▓▓▓ ▓▓ ▓    ▓ ▓▓ ▓ ▓  ▓ ▓┃    ┃▓▓▓▓   ▓▓▓▓       ░  ▓▓▓▓       ┃
┃▓▓▓ ▓   ▓ ▓    ▓ ▓▓▓  ▓▓▓   ▓▓  ┃    ┃▓▓▓▓   ▓▓▓▓       ▓▓ ▓▓▓▓       ┃
┃▓▓ ▓  ▓▓ ▓ ▓   ▓  ▓▓ ▓    ▓▓   ▓┃    ┃▓▓▓▓░░▓▓▓▓▓      ▓▓▓       ▓▓▓  ┃
┃▓▓▓ ▓▓▓▓ ▓▓▓   ▓ ▓     ▓▓▓ ▓▓▓ ▓┃    ┃▓▓▓▓░░▓▓▓▓▓▓   ▓▓▓      ▓▓▓▓▓▓▓▓┃
┃▓ ▓      ▓▓▓ ▓ ▓▓▓   ▓ ▓ ▓▓▓▓▓▓▓┃    ┃▓▓▓      ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓┃
┃▓▓▓ ▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓    ┃    ┃▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓   ┃
┃▓▓▓   ▓  ▓▓ ▓▓▓▓▓  ▓     ▓▓ ▓ ▓ ┃    ┃▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ┃
┃▓▓▓▓▓▓  ▓▓▓▓▓ ▓  ▓▓ ▓▓     ▓    ┃    ┃▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ┃
┃▓▓  ▓ ▓ ▓▓▓   ▓ ▓  ▓▓▓ ▓▓▓▓▓ ▓  ┃    ┃▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓    ┃
┃▓▓ ▓  ▓ ▓  ▓▓▓▓▓▓ ▓ ▓ ▓   ▓  ▓  ┃    ┃▓▓          ▓▓▓▓▓▓▓▓▓▓▓   ▓▓    ┃
┃ ▓  ▓    ▓   ▓▓▓▓ ▓▓▓▓▓ ▓ ▓▓ ▓▓ ┃    ┃▓▓          ▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃▓▓  ▓ ▓  ▓▓ ▓▓▓▓ ▓ ▓▓ ▓▓▓    ▓  ┃    ┃▓▓           ▓▓▓▓▓▓▓▓▓▓▓▓       ┃
┃▓ ▓  ▓ ▓▓ ▓  ▓  ▓▓▓▓▓▓  ▓▓▓▓▓▓  ┃    ┃      ▓▓▓    ▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓  ┃
┃ ▓▓▓▓ ▓▓▓    ▓▓ ▓▓  ▓  ▓ ▓  ▓▓ ▓┃    ┃  ▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓    ▓▓▓▓▓▓  ┃
┃▓ ▓▓ ▓ ▓ ▓    ▓▓▓ ▓▓    ▓▓▓ ▓   ┃    ┃  ▓▓▓▓▓▓▓    ▓▓▓▓▓▓     ▓▓▓▓▓   ┃
┃    ▓▓▓▓  ▓ ▓▓▓  ▓ ▓ ▓▓ ▓▓ ▓▓  ▓┃    ┃     ▓▓▓▓░░░░▓▓      ▓▓▓▓▓▓▓▓   ┃
┃  ▓  ▓▓▓▓▓ ▓      ▓  ▓▓▓▓▓▓▓   ▓┃    ┃     ▓▓▓▓░░░░        ▓▓▓▓▓▓▓▓   ┃
┃▓  ▓   ▓▓  ▓▓       ▓▓▓ ▓▓▓▓ ▓▓ ┃    ┃     ▓▓▓▓  ░         ▓▓▓▓▓▓▓▓▓  ┃
┃ ▓  ▓▓▓▓▓ ▓ ▓ ▓  ▓▓▓  ▓▓ ▓▓▓▓ ▓ ┃    ┃   ▓▓▓▓▓▓  ▓     ▓▓   ▓▓▓▓▓▓▓▓  ┃
┃  ▓▓▓  ▓▓ ▓▓ ▓  ▓▓    ▓▓ ▓▓▓▓ ▓ ┃    ┃   ▓▓  ▓▓▓▓▓    ▓▓▓   ▓▓▓▓▓▓▓▓  ┃
┃▓  ▓▓   ▓▓▓ ▓  ▓▓▓▓    ▓▓▓ ▓▓  ▓┃    ┃   ▓▓  ▓▓▓▓▓    ▓▓▓    ▓▓▓▓▓▓▓  ┃
┃   ▓ ▓ ▓▓▓▓ ▓ ▓ ▓▓ ▓▓  ▓ ▓  ▓▓▓ ┃    ┃        ▓▓▓▓░░░▓▓▓▓    ▓▓▓▓▓▓▓▓▓┃
┃    ▓    ▓▓▓ ▓▓    ▓ ▓ ▓▓▓ ▓▓ ▓▓┃    ┃        ▓▓▓▓░░▓▓▓▓     ▓▓▓▓▓▓▓▓▓┃
┃▓ ▓▓    ▓▓    ▓▓▓▓  ▓ ▓ ▓▓ ▓▓  ▓┃    ┃        ▓▓    ▓▓▓▓     ▓▓▓▓▓▓▓▓ ┃
┃▓  ▓ ▓▓▓▓  ▓▓  ▓▓▓▓ ▓  ▓▓ ▓▓ ▓▓ ┃    ┃              ▓▓▓▓▓▓▓ ░▓▓▓▓▓▓▓  ┃
┃  ▓▓  ▓   ▓▓  ▓▓▓  ▓▓ ▓ ▓   ▓  ▓┃    ┃          ▓▓  ▓▓▓▓▓▓▓       ▓▓  ┃
┃▓   ▓     ▓▓▓ ▓ ▓▓ ▓▓  ▓▓    ▓▓ ┃    ┃          ▓▓   ▓▓▓▓▓▓       ▓▓  ┃
┃▓ ▓▓   ▓         ▓▓▓    ▓ ▓▓▓▓  ┃    ┃                 ▓▓▓        ▓▓  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓ ▓ ▓▓   ▓   ▓▓▓ ▓▓▓  ▓▓▓▓      ┃    ┃              ▓▓      ▓▓▓       ┃
┃ ▓    ▓  ▓▓▓ ▓ ▓▓   ▓ ▓▓ ▓  ▓▓  ┃    ┃         ▓▓▓  ▓▓      ▓▓▓       ┃
┃▓    ▓▓ ▓▓ ▓▓  ▓    ▓ ▓   ▓▓ ▓  ┃    ┃     ▓▓▓▓▓▓▓          ▓▓    ▓▓  ┃
┃ ▓  ▓▓ ▓▓▓   ▓   ▓▓▓  ▓▓   ▓ ▓▓ ┃    ┃     ▓▓▓▓▓▓        ▓▓▓▓     ▓▓▓ ┃
┃▓  ▓  ▓ ▓▓ ▓   ▓▓  ▓▓▓▓     ▓▓▓ ┃    ┃       ▓▓▓     ▓▓  ▓▓▓▓     ▓▓▓ ┃
┃  ▓ ▓  ▓  ▓▓ ▓▓▓▓▓      ▓▓ ▓▓   ┃    ┃           ▓▓▓▓▓▓       ▓▓      ┃
┃ ▓  ▓  ▓▓   ▓▓      ▓  ▓▓▓      ┃    ┃           ▓▓▓▓        ░▓▓      ┃
┃ ▓▓▓      ▓▓▓▓▓     ▓▓▓▓   ▓    ┃    ┃ ▓▓        ▓▓▓                  ┃
┃▓▓▓ ▓▓  ▓▓ ▓▓    ▓ ▓   ▓  ▓  ▓▓ ┃    ┃ ▓▓        ▓▓                   ┃
┃▓ ▓  ▓▓▓ ▓    ▓▓▓ ▓  ▓ ▓   ▓▓ ▓ ┃    ┃                                ┃
┃ ▓ ▓    ▓      ▓ ▓ ▓▓      ▓ ▓▓▓┃    ┃                  ░░▓▓          ┃
┃▓▓▓▓  ▓▓▓  ▓  ▓▓▓ ▓ ▓▓  ▓ ▓ ▓  ▓┃    ┃  ▓▓  ▓▓▓     ▓▓▓░░░▓▓          ┃
┃  ▓▓  ▓▓▓ ▓ ▓  ▓ ▓  ▓▓  ▓ ▓     ┃    ┃  ▓▓  ▓▓▓     ▓▓▓░  ▓▓          ┃
┃▓ ▓   ▓   ▓   ▓▓▓   ▓ ▓▓    ▓▓  ┃    ┃  ░░  ▓▓▓     ▓▓▓▓  ▓▓▓▓    ▓▓  ┃
┃   ▓ ▓▓ ▓▓ ▓▓ ▓▓ ▓  ▓▓▓ ▓  ▓▓▓ ▓┃    ┃  ░░▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓   ▓▓▓ ┃
┃▓ ▓ ▓▓ ▓ ▓  ▓▓ ▓▓▓ ▓  ▓▓  ▓  ▓▓▓┃    ┃  ░▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓   ▓▓▓ ┃
┃▓▓  ▓ ▓▓ ▓▓▓▓▓▓ ▓      ▓▓ ▓ ▓   ┃    ┃  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓  ┃
┃  ▓ ▓▓ ▓▓  ▓  ▓ ▓ ▓▓▓ ▓ ▓▓▓▓ ▓  ┃    ┃  ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  ┃
┃ ▓▓▓   ▓▓   ▓▓▓▓ ▓▓▓▓▓▓  ▓▓ ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓┃
┃ ▓▓ ▓▓ ▓ ▓▓ ▓    ▓  ▓▓▓▓    ▓▓▓▓┃    ┃ ▓▓▓▓▓▓▓▓▓  ▓    ▓▓▓▓▓▓▓    ▓▓▓▓┃
┃▓ ▓ ▓▓ ▓ ▓  ▓  ▓▓ ▓▓▓ ▓▓   ▓ ▓  ┃    ┃ ▓▓▓▓▓░▓▓▓▓▓▓    ▓▓▓▓▓▓▓    ░░░░┃
┃▓▓ ▓   ▓▓▓▓▓▓   ▓  ▓▓▓  ▓▓▓   ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓     ░░░░┃
┃▓▓ ▓ ▓▓  ▓▓  ▓▓ ▓▓ ▓▓ ▓  ▓ ▓▓▓ ▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓     ▓▓▓▓▓▓▓  ▓▓▓▓▓▓░┃
┃  ▓▓▓ ▓▓  ▓   ▓  ▓▓ ▓▓   ▓▓▓▓ ▓ ┃    ┃   ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓┃
┃▓  ▓▓▓ ▓ ▓  ▓▓▓▓ ▓▓ ▓▓▓▓▓   ▓  ▓┃    ┃   ▓▓▓▓▓▓▓   ▓▓▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓┃
┃ ▓   ▓ ▓▓  ▓    ▓ ▓▓  ▓▓▓   ▓▓▓ ┃    ┃     ▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓   ▓▓▓▓┃
┃▓▓    ▓  ▓▓   ▓▓▓   ▓▓▓ ▓▓▓▓  ▓▓┃    ┃     ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓   ▓▓▓┃
┃ ▓▓▓▓▓ ▓▓▓▓  ▓▓  ▓▓ ▓▓   ▓  ▓ ▓▓┃    ┃▓▓▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓  ▓▓    ▓▓┃
┃▓ ▓▓ ▓ ▓  ▓▓     ▓ ▓▓   ▓▓     ▓┃    ┃▓▓▓▓▓▓▓▓  ▓      ▓▓▓▓▓        ▓▓┃
┃▓▓▓▓ ▓▓   ▓ ▓▓▓ ▓ ▓▓ ▓▓       ▓▓┃    ┃▓▓▓▓▓▓▓▓  ▓▓▓▓▓  ▓▓▓▓▓          ┃
┃ ▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓ ▓▓  ▓▓  ▓   ┃    ┃▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓          ┃
┃▓ ▓▓▓▓▓▓     ▓ ▓   ▓▓▓▓   ▓▓ ▓▓▓┃    ┃ ▓▓▓▓▓▓▓            ▓▓          ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓ ▓     ▓      ▓▓ ▓▓▓▓▓▓ ▓ ▓▓  ┃    ┃                ▓▓   ▓▓▓        ┃
┃ ▓▓  ▓ ▓▓▓   ▓▓▓▓▓  ▓ ▓ ▓ ▓     ┃    ┃             ▓▓▓▓▓▓▓▓▓▓▓        ┃
┃ ▓      ▓  ▓▓▓▓▓  ▓▓ ▓▓  ▓ ▓    ┃    ┃            ▓▓▓▓▓▓▓▓▓▓▓▓        ┃
┃▓  ▓▓▓▓▓  ▓ ▓▓ ▓▓ ▓▓  ▓▓     ▓▓ ┃    ┃      ▓▓▓   ▓▓▓▓▓▓▓▓  ▓▓        ┃
┃ ▓▓   ▓▓▓  ▓ ▓ ▓▓ ▓    ▓  ▓  ▓ ▓┃    ┃ ▓▓▓░░▓▓▓   ▓▓▓▓▓     ▓▓        ┃
┃▓▓▓▓▓  ▓▓▓ ▓ ▓     ▓▓▓▓▓▓▓▓▓▓ ▓▓┃    ┃ ▓▓▓░░▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓      ┃
┃ ▓▓ ▓ ▓▓▓▓   ▓▓ ▓▓  ▓▓ ▓  ▓     ┃    ┃ ▓▓▓░░▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓▓     ┃
┃▓  ▓ ▓▓ ▓▓▓▓▓▓ ▓ ▓  ▓▓ ▓▓  ▓ ▓▓ ┃    ┃ ▓▓▓░░▓▓▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓    ┃
┃ ▓▓▓▓  ▓▓  ▓ ▓▓▓   ▓  ▓ ▓▓▓▓▓ ▓ ┃    ┃ ▓▓     ▓▓▓▓▓▓▓▓    ▓▓▓▓▓▓▓▓▓   ┃
┃ ▓ ▓     ▓▓   ▓▓   ▓▓▓▓▓ ▓ ▓ ▓  ┃    ┃ ░░     ▓▓▓▓  ▓▓    ▓▓▓▓▓▓▓▓▓   ┃
┃  ▓  ▓  ▓▓ ▓   ▓ ▓       ▓ ▓▓ ▓ ┃    ┃ ░░     ▓▓▓▓            ▓▓▓▓▓   ┃
┃▓▓   ▓ ▓▓ ▓▓▓▓▓  ▓▓ ▓▓  ▓▓  ▓  ▓┃    ┃▓▓▓  ▓▓▓▓▓▓▓▓▓          ▓▓▓     ┃
┃▓▓▓ ▓▓▓▓▓▓  ▓▓ ▓   ▓ ▓▓▓▓▓▓     ┃    ┃▓▓▓▓▓▓▓▓▓▓▓░▓▓     ▓▓▓▓▓▓▓▓     ┃
┃▓  ▓ ▓▓ ▓▓▓       ▓▓▓ ▓▓ ▓▓ ▓ ▓ ┃    ┃ ▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓     ┃
┃ ▓▓▓▓▓▓▓▓  ▓     ▓▓  ▓  ▓   ▓  ▓┃    ┃  ▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓      ┃
┃  ▓  ▓▓    ▓▓   ▓▓ ▓ ▓▓▓▓▓  ▓▓▓ ┃    ┃     ▓▓▓▓        ▓▓▓  ▓▓▓▓  ▓▓▓ ┃
┃▓ ▓  ▓▓▓ ▓  ▓  ▓   ▓    ▓▓ ▓ ▓  ┃    ┃     ▓▓▓▓             ▓▓▓▓  ▓▓▓ ┃
┃▓▓ ▓▓  ▓▓▓▓▓      ▓▓  ▓▓▓▓ ▓ ▓▓▓┃    ┃     ▓▓▓▓▓            ▓▓▓▓░░▓▓▓▓┃
┃▓   ▓ ▓ ▓▓   ▓   ▓   ▓▓▓ ▓ ▓ ▓▓▓┃    ┃▓▓    ▓▓▓▓            ▓▓▓▓░░▓▓▓▓┃
┃▓▓ ▓  ▓▓▓▓    ▓▓▓▓▓    ▓▓▓▓ ▓  ▓┃    ┃▓▓     ▓▓▓   ▓▓▓░     ▓▓▓▓░░░░  ┃
┃▓▓ ▓      ▓ ▓▓▓▓  ▓▓  ▓▓▓▓ ▓ ▓  ┃    ┃▓▓     ▓▓▓   ▓▓▓      ▓▓▓▓░░░   ┃
┃  ▓  ▓▓ ▓▓▓ ▓ ▓    ▓ ▓▓▓   ▓▓▓ ▓┃    ┃      ▓▓▓▓   ░░      ▓▓▓▓▓      ┃
┃▓     ▓▓  ▓    ▓     ▓ ▓▓ ▓   ▓ ┃    ┃      ▓▓▓    ░░      ▓▓▓▓▓      ┃
┃▓  ▓  ▓▓▓   ▓ ▓   ▓▓▓▓ ▓ ▓▓  ▓▓ ┃    ┃      ▓▓▓    ░░    ▓▓▓▓▓▓       ┃
┃ ▓▓▓▓▓  ▓ ▓▓ ▓▓     ▓ ▓▓▓   ▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓       ┃
┃▓▓▓  ▓▓ ▓  ▓ ▓ ▓   ▓▓▓▓▓▓ ▓▓▓  ▓┃    ┃ ▓▓▓▓▓▓▓▓   ▓▓▓    ▓▓▓▓▓▓ ▓▓▓   ┃
┃  ▓ ▓▓ ▓  ▓ ▓▓    ▓▓▓▓ ▓  ▓▓▓▓  ┃    ┃ ▓▓▓▓▓▓▓▓         ▓▓▓▓▓▓▓ ▓▓▓   ┃
┃ ▓▓ ▓ ▓ ▓      ▓ ▓▓▓  ▓▓▓ ▓▓▓ ▓▓┃    ┃ ▓▓▓▓▓░▓░         ▓▓▓▓▓▓▓ ▓▓▓▓▓ ┃
┃ ▓ ▓ ▓ ▓ ▓▓▓ ▓▓    ▓▓▓▓ ▓ ▓  ▓▓ ┃    ┃ ▓▓▓▓░░▓▓▓▓▓▓▓▓    ▓▓▓▓▓    ▓▓▓ ┃
┃▓▓   ▓▓▓▓▓▓▓▓▓▓      ▓▓    ▓ ▓▓ ┃    ┃       ▓▓▓▓▓▓▓▓    ▓▓▓▓▓    ▓▓▓ ┃
┃  ▓     ▓  ▓  ▓▓  ▓ ▓  ▓ ▓ ▓ ▓ ▓┃    ┃            ▓▓▓           ░▓▓▓▓ ┃
┃▓▓ ▓ ▓▓  ▓  ▓▓ ▓   ▓  ▓▓▓ ▓▓▓▓▓▓┃    ┃                           ▓▓▓▓ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃▓  ▓▓▓ ▓▓ ▓     ▓▓▓▓▓▓▓▓▓  ▓▓ ▓ ┃    ┃????????????????????????????????┃
┃ ▓ ▓  ▓  ▓▓ ▓ ▓▓▓▓ ▓ ▓▓▓▓▓▓ ▓▓▓ ┃    ┃????????????????????????????????┃
┃▓ ▓      ▓▓ ▓  ▓▓▓▓▓ ▓▓▓▓▓▓▓  ▓ ┃    ┃????????????????????????????????┃
┃▓▓▓▓▓  ▓▓▓  ▓ ▓ ▓ ▓▓▓▓▓▓▓▓▓ ▓ ▓ ┃    ┃????????????????????????????????┃
┃▓ ▓▓▓ ▓▓ ▓▓  ▓  ▓   ▓▓ ▓▓▓ ▓    ┃    ┃????????????????????????????????┃
┃▓ ▓ ▓▓▓▓   ▓  ▓ ▓▓     ▓▓  ▓ ▓  ┃    ┃????????????????????????????????┃
┃▓ ▓▓     ▓▓    ▓▓ ▓ ▓ ▓▓▓▓▓▓ ▓▓▓┃    ┃????????????????????????????????┃
┃   ▓▓▓▓ ▓    ▓ ▓ ▓    ▓▓     ▓  ┃    ┃????????????????????????????????┃
┃▓▓  ▓▓   ▓▓▓▓ ▓ ▓ ▓▓ ▓   ▓  ▓▓  ┃    ┃????????????????????????????????┃
┃▓▓▓       ▓ ▓▓▓▓▓▓▓     ▓ ▓ ▓▓  ┃    ┃????????????????????????????????┃
┃▓▓ ▓   ▓ ▓  ▓▓   ▓▓▓▓▓ ▓ ▓    ▓▓┃    ┃????????????????????????????????┃
┃   ▓▓ ▓ ▓▓▓   ▓ ▓ ▓ ▓  ▓ ▓▓▓▓   ┃    ┃????????????????????????????????┃
┃▓   ▓   ▓▓  ▓ ▓▓▓         ▓▓ ▓ ▓┃    ┃????????????????????????????????┃
┃  ▓ ▓▓ ▓▓▓▓   ▓▓▓ ▓ ▓ ▓▓     ▓  ┃    ┃????????????????????????????????┃
┃ ▓▓▓▓ ▓ ▓▓ ▓  ▓  ▓ ▓ ▓ ▓    ▓▓▓▓┃    ┃????????????????????????????????┃
┃▓▓   ▓      ▓    ▓▓ ▓   ▓ ▓ ▓▓ ▓┃    ┃????????????????????????????????┃
┃▓ ▓ ▓ ▓ ▓  ▓ ▓▓▓▓     ▓▓▓▓▓▓  ▓▓┃    ┃????????????????????????????????┃
┃▓▓ ▓▓ ▓▓▓ ▓▓▓▓ ▓  ▓     ▓  ▓   ▓┃    ┃????????????????????????????????┃
┃▓ ▓  ▓▓▓ ▓    ▓    ▓  ▓▓▓  ▓    ┃    ┃????????????????????????????????┃
┃   ▓▓▓   ▓▓ ▓   ▓ ▓▓ ▓▓  ▓▓ ▓ ▓▓┃    ┃????????????????????????????????┃
┃▓  ▓▓  ▓▓  ▓ ▓▓   ▓▓▓▓▓    ▓  ▓▓┃    ┃????????????????????????????????┃
┃   ▓  ▓▓   ▓▓ ▓ ▓▓▓   ▓  ▓ ▓▓▓▓▓┃    ┃????????????????????????????????┃
┃▓     ▓▓ ▓▓▓ ▓▓▓▓▓ ▓▓▓  ▓ ▓  ▓  ┃    ┃????????????????????????????????┃
┃▓▓    ▓   ▓ ▓ ▓  ▓▓ ▓ ▓ ▓▓   ▓ ▓┃    ┃????????????????????????????????┃
┃ ▓▓    ▓▓▓▓▓▓▓  ▓ ▓ ▓▓▓       ▓ ┃    ┃????????????????????????????????┃
┃ ▓  ▓▓▓  ▓▓  ▓    ▓▓▓▓▓▓ ▓▓▓   ▓┃    ┃????????????????????????????????┃
┃▓ ▓▓▓  ▓▓     ▓ ▓  ▓▓ ▓▓   ▓ ▓▓▓┃    ┃????????????????????????????????┃
┃ ▓▓ ▓  ▓   ▓▓ ▓▓▓ ▓▓▓▓▓ ▓ ▓ ▓ ▓ ┃    ┃????????????????????????????????┃
┃▓▓            ▓ ▓▓▓    ▓▓ ▓▓   ▓┃    ┃????????????????????????????????┃
┃▓ ▓ ▓▓▓▓▓ ▓▓▓ ▓  ▓    ▓  ▓▓▓▓ ▓ ┃    ┃????????????????????????????????┃
┃  ▓ ▓▓▓      ▓▓▓  ▓ ▓▓ ▓▓  ▓ ▓▓ ┃    ┃????????????????????????????????┃
┃▓   ▓   ▓▓  ▓ ▓▓▓  ▓▓  ▓▓▓     ▓┃    ┃????????????????????????????????┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓ ▓▓ ▓▓▓▓▓ ▓▓▓ ▓   ▓  ▓▓▓▓▓ ▓▓┃    ┃????????????????????????????????┃
┃▓ ▓▓     ▓▓ ▓ ▓ ▓   ▓▓▓▓ ▓     ▓┃    ┃????????????????????????????????┃
┃▓  ▓   ▓▓▓  ▓▓  ▓▓ ▓▓▓▓▓▓ ▓   ▓▓┃    ┃????????????????????????????????┃
┃ ▓▓  ▓  ▓   ▓  ▓ ▓▓     ▓▓▓ ▓ ▓ ┃    ┃????????????????????????????????┃
┃        ▓ ▓▓ ▓  ▓▓ ▓   ▓▓ ▓▓▓ ▓ ┃    ┃????????????????????????????????┃
┃ ▓ ▓  ▓▓▓▓▓ ▓▓ ▓ ▓ ▓▓▓▓▓ ▓▓ ▓▓ ▓┃    ┃????????????????????????????????┃
┃▓      ▓▓▓▓▓   ▓      ▓▓▓▓▓▓▓ ▓▓┃    ┃????????????????????????????????┃
┃    ▓▓ ▓▓▓  ▓▓ ▓     ▓ ▓▓▓▓ ▓▓  ┃    ┃????????????????????????????????┃
┃  ▓▓ ▓ ▓▓  ▓ ▓▓▓  ▓ ▓   ▓▓▓ ▓   ┃    ┃????????????????????????????????┃
┃ ▓      ▓  ▓▓▓  ▓  ▓▓      ▓  ▓▓┃    ┃????????????????????????????????┃
┃ ▓▓  ▓▓ ▓▓  ▓▓  ▓ ▓  ▓ ▓  ▓▓▓▓  ┃    ┃????????????????????????????????┃
┃▓       ▓▓    ▓   ▓ ▓ ▓ ▓▓▓▓ ▓  ┃    ┃????????????????????????????????┃
┃▓▓ ▓  ▓▓ ▓      ▓ ▓▓▓     ▓ ▓   ┃    ┃????????????????????????????????┃
┃ ▓▓▓▓     ▓ ▓    ▓ ▓▓ ▓ ▓▓▓ ▓▓▓▓┃    ┃????????????????????????????????┃
┃▓▓    ▓▓   ▓▓ ▓▓  ▓  ▓▓ ▓ ▓▓▓▓▓▓┃    ┃????????????????????????????????┃
┃▓ ▓▓ ▓  ▓▓▓   ▓▓▓  ▓ ▓ ▓     ▓  ┃    ┃????????????????????????????????┃
┃▓▓ ▓ ▓▓▓▓▓▓▓▓▓▓ ▓  ▓▓   ▓   ▓ ▓ ┃    ┃????????????????????????????????┃
┃▓▓ ▓▓ ▓ ▓▓ ▓  ▓▓    ▓▓▓▓▓ ▓▓▓▓▓▓┃    ┃????????????????????????????????┃
┃ ▓  ▓▓▓  ▓       ▓ ▓         ▓ ▓┃    ┃????????????????????????????????┃
┃ ▓▓       ▓▓ ▓▓  ▓     ▓ ▓ ▓ ▓▓ ┃    ┃????????????????????????????????┃
┃ ▓▓▓ ▓▓▓ ▓ ▓ ▓ ▓▓▓ ▓      ▓ ▓▓ ▓┃    ┃????????????????????????????????┃
┃   ▓ ▓ ▓▓▓▓▓  ▓  ▓▓    ▓   ▓▓   ┃    ┃????????????????????????????????┃
┃  ▓ ▓ ▓▓▓▓▓▓▓▓▓▓▓ ▓▓▓ ▓  ▓▓   ▓ ┃    ┃????????????????????????????????┃
┃▓ ▓  ▓    ▓  ▓▓ ▓▓  ▓▓▓▓  ▓▓▓ ▓▓┃    ┃????????????????????????????????┃
┃  ▓▓▓▓▓ ▓ ▓  ▓   ▓   ▓  ▓▓   ▓  ┃    ┃????????????????????????????????┃
┃▓  ▓▓ ▓▓   ▓    ▓▓     ▓ ▓▓▓  ▓▓┃    ┃????????????????????????????????┃
┃ ▓▓▓▓▓▓ ▓ ▓ ▓▓ ▓       ▓▓▓ ▓▓ ▓ ┃    ┃????????????????????????????????┃
┃ ▓▓ ▓▓ ▓▓ ▓▓▓ ▓▓  ▓▓      ▓ ▓▓  ┃    ┃????????????????????????????????┃
┃  ▓▓ ▓ ▓▓    ▓ ▓▓▓ ▓  ▓▓▓▓▓▓   ▓┃    ┃????????????????????????????????┃
┃▓  ▓    ▓▓▓ ▓ ▓   ▓   ▓ ▓▓ ▓  ▓▓┃    ┃????????????????????????????????┃
┃ ▓▓ ▓    ▓▓▓  ▓ ▓▓▓▓▓▓    ▓   ▓ ┃    ┃????????????????????????????????┃
┃ ▓▓▓ ▓▓   ▓ ▓ ▓   ▓  ▓▓▓▓▓   ▓▓ ┃    ┃????????????????????????????????┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

              input:                                output:
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ▓▓  ▓   ▓▓ ▓ ▓▓ ▓▓ ▓  ▓▓ ▓ ▓ ▓ ┃    ┃????????????????????????????????┃
┃  ▓   ▓▓ ▓  ▓▓▓  ▓▓▓ ▓▓  ▓▓▓▓▓  ┃    ┃????????????????????????????????┃
┃ ▓ ▓ ▓  ▓▓▓▓▓▓ ▓▓ ▓  ▓▓   ▓▓ ▓  ┃    ┃????????????????????????????????┃
┃   ▓▓  ▓▓▓▓  ▓▓▓ ▓ ▓ ▓▓▓▓▓▓ ▓ ▓▓┃    ┃????????????????????????????????┃
┃▓▓ ▓  ▓▓ ▓  ▓▓ ▓▓▓▓▓▓  ▓▓▓ ▓▓  ▓┃    ┃????????????????????????????????┃
┃▓    ▓ ▓ ▓▓ ▓▓▓ ▓▓    ▓   ▓▓    ┃    ┃????????????????????????????????┃
┃   ▓▓▓      ▓▓▓▓▓   ▓▓    ▓▓▓▓▓▓┃    ┃????????????????????????????????┃
┃     ▓▓▓    ▓  ▓  ▓ ▓  ▓ ▓▓▓▓ ▓▓┃    ┃????????????????????????????????┃
┃▓▓  ▓ ▓▓▓ ▓▓  ▓    ▓ ▓    ▓▓▓▓▓ ┃    ┃????????????????????????????????┃
┃  ▓▓▓▓  ▓ ▓ ▓▓▓  ▓  ▓  ▓ ▓ ▓▓▓▓▓┃    ┃????????????????????????????????┃
┃▓▓▓▓ ▓▓▓ ▓  ▓   ▓▓  ▓▓  ▓    ▓▓▓┃    ┃????????????????????????????????┃
┃▓   ▓ ▓       ▓ ▓  ▓▓   ▓  ▓▓▓ ▓┃    ┃????????????????????????????????┃
┃   ▓ ▓ ▓▓ ▓▓▓▓▓  ▓▓▓▓  ▓  ▓    ▓┃    ┃????????????????????????????????┃
┃▓▓    ▓  ▓▓ ▓▓▓▓  ▓ ▓ ▓ ▓▓      ┃    ┃????????????????????????????????┃
┃  ▓ ▓▓ ▓▓ ▓▓▓ ▓▓ ▓ ▓▓ ▓▓▓▓▓▓ ▓  ┃    ┃????????????????????????????????┃
┃  ▓▓  ▓   ▓ ▓▓▓▓ ▓▓  ▓  ▓ ▓  ▓▓ ┃    ┃????????????????????????????????┃
┃▓ ▓▓▓ ▓▓▓ ▓ ▓  ▓▓ ▓ ▓    ▓ ▓▓▓▓ ┃    ┃????????????????????????????????┃
┃▓▓▓   ▓   ▓ ▓▓▓▓▓ ▓ ▓▓  ▓▓    ▓▓┃    ┃????????????????????????????????┃
┃▓▓▓▓    ▓▓ ▓ ▓▓▓ ▓▓ ▓▓▓ ▓ ▓▓▓   ┃    ┃????????????????????????????????┃
┃▓      ▓  ▓ ▓  ▓ ▓ ▓ ▓  ▓▓▓ ▓▓▓▓┃    ┃????????????????????????????????┃
┃  ▓       ▓▓▓ ▓▓▓ ▓▓▓  ▓▓▓▓   ▓▓┃    ┃????????????????????????????????┃
┃     ▓▓ ▓ ▓▓▓▓    ▓▓ ▓▓  ▓    ▓ ┃    ┃????????????????????????????????┃
┃▓ ▓▓▓▓ ▓▓ ▓ ▓ ▓▓  ▓ ▓   ▓  ▓▓▓  ┃    ┃????????????????????????????????┃
┃▓  ▓▓   ▓ ▓▓▓▓▓▓▓ ▓ ▓ ▓ ▓ ▓▓▓▓▓ ┃    ┃????????????????????????????????┃
┃▓ ▓▓▓ ▓▓ ▓ ▓  ▓ ▓ ▓▓  ▓▓ ▓▓▓▓▓▓ ┃    ┃????????????????????????????????┃
┃▓▓  ▓▓   ▓▓    ▓▓▓▓▓▓▓   ▓▓▓▓ ▓▓┃    ┃????????????????????????????????┃
┃▓▓ ▓▓    ▓▓▓ ▓▓   ▓ ▓▓ ▓▓▓▓  ▓  ┃    ┃????????????????????????????????┃
┃  ▓  ▓▓ ▓  ▓▓  ▓▓▓▓ ▓    ▓▓  ▓  ┃    ┃????????????????????????????????┃
┃ ▓ ▓▓▓ ▓ ▓▓▓ ▓ ▓  ▓ ▓▓ ▓▓▓▓▓▓▓▓▓┃    ┃????????????????????????????????┃
┃▓ ▓▓ ▓ ▓▓   ▓▓▓ ▓▓▓ ▓ ▓▓▓▓  ▓   ┃    ┃????????????????????????????????┃
┃  ▓ ▓▓ ▓▓ ▓  ▓     ▓▓▓   ▓▓ ▓ ▓▓┃    ┃????????????????????????????????┃
┃      ▓▓ ▓▓ ▓ ▓▓   ▓  ▓▓  ▓    ▓┃    ┃????????????????????????????????┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛