r2-d2.txt

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠴⠶⢶⠶⢧⠧⠷⠶⠶⢖⠔⢄⠄⡄⠂⠀⠈⠐⢄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⢗⡱⣝⣦⡲⣔⢦⢧⡳⣅⠑⢟⢿⢿⣿⣯⣦⡰⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠫⣐⣞⢮⣗⣗⡯⡯⡯⣯⣻⣺⢢⠈⢝⣕⢯⡻⣽⢿⣻⣾⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢘⢻⠻⠻⠟⠗⢁⢜⢞⢮⡳⣳⢳⡫⡯⣻⢺⡺⣪⢳⢅⠀⢓⠗⠝⠎⠏⠓⠋⠓⢉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡜⡜⢜⢐⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢣⠧⡣⣱⣰⢤⢄⡄⣄⣀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⢪⡪⣵⣿⣿⣿⣿⣷⣝⢮⡺⣾⡽⡦⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠣⣣⣻⣿⣿⣫⣷⢿⣽⣗⢗⢽⣿⣽⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⢱⢱⢳⣿⣿⢱⣻⣜⣿⣿⢗⢽⢽⣷⡿⣷⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢪⢢⡟⢌⣿⣿⣽⣿⣾⢿⡫⡳⡳⣽⣗⣛⡯⠂⢀⠀⠠⠀⠠⠀⡐⠀⡂⠐⡀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢵⣥⠟⢌⢼⣗⡯⡿⡽⡕⡗⡝⡜⣎⣟⢾⣻⡗⠅⠠⠐⡀⠅⠂⡁⠄⡂⠄⠅⡐⠠⠨⢀⠁⡀⠀⠀⠀⠀⠀⠀⡀⣀⡠⡠⣔⢆⢞⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡟⡼⣝⠕⠙⠚⠝⠟⢞⢝⢞⢞⢎⢮⡿⣗⠟⠙⠨⠐⢐⠠⠨⣐⣔⣔⣤⣥⣕⢨⣬⣬⣦⣦⣦⠐⡴⣔⢦⣳⠘⣞⣞⡮⣯⢮⢯⡪⡪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢇⣣⢣⠃⢄⠄⣄⣀⣀⢀⢀⢀⠀⠁⠉⠁⡠⡪⠪⢈⠢⡂⢅⢪⣿⣿⣿⣿⣿⢌⣿⣿⣿⣿⣾⠄⣿⢮⡳⣝⡆⢽⡷⣿⣽⣯⣯⣗⢌⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣾⡱⡪⣝⠐⢸⠨⣗⣿⣺⣽⠫⡓⢽⢽⠀⣲⣟⡟⠧⡑⡄⠄⡣⣹⣿⣿⣿⣿⣿⢕⣿⣿⣿⣿⣿⡇⣺⣯⢟⢾⣕⠸⣿⣿⣷⡿⣾⢯⡳⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣸⣘⢕⢈⢸⠨⣻⣾⢷⡗⢅⠂⡂⣿⠀⢿⣽⣖⡄⣮⢢⡣⡺⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⢺⣿⢽⣝⣷⢘⣿⣿⣻⣟⡿⡻⡸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣮⣝⣝⠀⠸⠨⢿⢾⣟⣿⣢⣡⣼⢿⡀⠄⠣⣿⣺⣵⣳⠽⡝⣾⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣗⠹⢿⠳⠳⠻⢐⣛⣍⣥⣵⣺⣞⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡳⡻⣟⣇⢵⢷⡶⣶⢶⣦⣮⣬⣌⣭⣠⣌⣆⣦⣱⣱⣜⣵⣝⣮⣯⣯⣯⣫⣯⣵⣭⣮⣮⣮⣶⣶⣷⣖⡗⣗⡽⡿⣞⠯⠗⠻⠙⢌⠢⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡨⡂⡂⠀⠈⠁⠉⢋⠛⠳⠻⠞⠿⠿⠿⢿⢿⢿⡿⣿⣿⣿⣿⡿⣿⢿⡿⡿⡿⡿⡿⠿⢿⢻⢻⢙⠪⠁⠉⠀⠁⠁⠐⢈⠠⠁⠅⠢⠑⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢦⣢⣀⣀⠡⡐⢈⠐⠠⠡⠨⢐⠡⡑⡰⡑⡌⡖⣒⢖⢮⣺⣪⡳⣕⢕⢕⢕⢕⢝⢜⢌⠆⢕⠐⠀⠀⠀⠀⠠⠈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠻⠽⣳⢾⣞⣯⣯⣷⢷⣷⣵⣺⣲⣲⣲⣶⣵⣵⣵⣵⣷⣵⣧⣷⡕⡣⢃⠃⡃⠃⠅⠡⠁⠡⠁⡈⠀⠁⠀⠠⠀⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⣄⣀⡀⠀⠁⠉⠊⠋⠛⠓⠛⠟⠿⠿⢿⢿⢿⡿⣿⣿⢿⡿⣟⡿⡆⢂⠂⡂⠐⡈⡀⡂⡁⡂⠡⠠⠈⡀⠄⠂⡐⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠨⠀⣟⣷⡹⣵⣤⣄⣔⣷⣲⣦⣦⣤⣤⣔⣤⣄⣢⣐⣄⡐⡀⢂⠂⠂⢂⠐⠨⡀⠅⠂⠄⠄⠄⠂⠂⢂⠁⠄⢐⠐⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠌⢌⠀⠀⠑⠩⠓⠓⠛⠺⣽⢿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣽⢿⡅⠨⢐⠐⡈⠄⠡⠐⢈⠠⠁⠄⠂⠅⡂⢅⠇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣜⣗⣿⣺⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠨⡐⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠑⠙⠋⠓⢛⠺⠫⠻⠽⠺⢛⠙⢊⠋⢋⠂⠅⠄⠅⠄⠅⠨⠐⢀⠂⠨⠀⠅⠅⢜⢌⠇⠀⡀⠀⢐⠀⠀⠀⠀⠀⢰⢕⡗⣗⣷⡃⢘⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠄⠀⠁⠀⡁⠢⠀⣳⢧⡶⡕⢦⢦⣤⣠⣀⣀⢀⠂⡈⠀⠄⠂⢐⠀⡂⢐⠈⠄⢂⠢⠨⠐⠨⠠⠁⢅⠡⠈⠄⠠⠁⠌⠌⢌⢢⢱⠅⠐⢀⠈⠠⠐⠈⢀⡠⠄⢸⢱⢝⣞⡾⡂⢸⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂⠠⠡⠀⠘⠙⢟⡇⡯⣿⡾⣷⣿⣽⡿⣿⣽⣄⣦⣥⣴⣴⢶⣲⣴⣵⡴⣤⡅⠌⠄⠅⠡⠡⠀⠅⡈⠄⠡⠨⢈⠢⡱⢸⠨⠐⠀⠄⡁⠂⡁⠄⡇⡇⠈⢎⣦⣽⣽⣧⢰⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠂⠀⠨⠨⠀⠁⠀⠀⠁⠉⠓⠛⠟⠾⢯⢿⣻⣗⠛⠗⠿⢾⣻⢿⣻⣯⣷⢿⣻⢎⠐⠠⠡⠁⡅⠌⡀⠂⠌⠄⡑⠄⡣⡊⢎⠆⡈⠐⠠⠠⠁⠠⠐⠉⠀⣦⣿⣿⣿⣿⣿⢿⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠀⠂⠈⠠⠡⠁⠐⠀⠀⠀⢀⠀⠂⠐⠀⠄⠀⢀⠀⠌⠠⢁⢀⠀⠍⠨⠈⠄⠡⢀⠂⠌⠄⠅⡁⠆⠂⠄⠡⠨⢐⠠⢑⢌⠪⡪⡂⠄⢁⠂⠨⢀⠡⢀⢔⢂⣿⣿⣿⣿⣿⣿⣿⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⡀⡂⡐⢈⠌⡂⠀⠄⠀⠀⢀⠀⡷⡶⡲⠴⠴⡤⣤⣨⣀⠂⠄⠀⠅⠡⠁⠅⡁⡂⠌⠌⠄⠅⡂⢅⠡⢁⠡⢈⢐⠨⡐⢌⢪⢸⠐⡈⠠⠀⠅⢂⠀⡂⡇⡅⣿⣿⣿⣿⣿⣿⡿⡎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢪⡜⡔⡕⠄⢀⠀⠄⠀⠀⠀⡏⣾⣞⢟⢞⢮⢪⣻⣗⠠⠁⠐⢈⠐⡁⠅⢂⠂⠅⡑⠨⢐⠠⡁⡂⡐⢐⠐⡐⠐⢌⠢⡣⢪⢂⠐⡀⠅⠨⠀⢂⠀⠁⡀⣿⣿⣿⣿⣿⣿⠙⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢑⠑⡁⠠⠀⢀⠀⠈⠀⢎⣿⢞⠟⡗⠷⢷⢸⣽⠀⠅⢈⠀⡂⡐⡈⠄⠌⡐⠠⢁⢂⠂⡢⠐⡀⢂⠂⠌⠌⠢⡑⢜⢸⢐⠠⠐⡀⠅⠨⠀⠂⠁⠀⣿⣻⣿⣿⣻⣿⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀⠂⠘⢕⠆⡀⠀⠀⠁⡱⣻⢟⢗⢞⠮⡶⡸⣾⢈⢐⠠⠐⠠⠐⠠⠨⢐⠠⢁⠂⠔⡐⠄⠅⢂⠂⠌⡐⠡⢑⠌⠪⡸⡐⡀⢂⠐⠨⠀⠅⠂⠀⠂⣿⢿⣿⣯⣿⣽⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢀⠁⡘⠲⡤⠀⠂⠈⡀⢜⠽⣿⡻⡚⠖⠶⡸⣽⡂⡐⢀⠂⠡⠨⠠⢁⠂⠌⡐⠨⢐⠠⢑⠨⠐⠨⢐⠠⠑⠄⠅⠅⡊⠜⡜⡔⡥⡱⡑⡌⢔⠀⠀⣿⣿⣿⣿⡞⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠐⢵⡄⢂⠠⠀⠄⢸⣿⡬⣭⣝⣕⣵⣻⣿⡂⡐⢐⠈⠄⠡⢈⢐⠨⢐⠠⢁⠢⠨⢐⠠⠁⠅⡂⠌⠨⠨⠨⢐⠠⡑⡱⣹⢸⢝⢝⢼⡐⣱⣀⣿⣿⣿⡯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠂⠁⢦⣌⠀⠄⠀⠂⢸⢰⣗⣗⣶⢵⡹⣻⣽⠆⠨⠠⠈⠌⠨⠐⡀⡂⢂⠌⡐⠨⢐⢐⠨⢈⢐⠠⠁⠅⡡⢁⠂⡐⡐⢌⢞⠆⠅⢕⢑⠐⢼⣿⣿⣿⣟⢇⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡈⠄⠁⢦⢌⠀⠂⠀⡁⢐⢯⡿⡎⣾⣻⣿⢌⢿⡃⠅⠌⠄⠅⠌⡐⠠⢂⠂⡂⡂⡑⠠⠢⢈⢐⠠⠈⠌⡐⢐⠐⡀⠂⠄⢅⢻⢌⠪⠐⠄⢅⢳⣿⣿⣿⣷⡃⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⠁⢦⢩⠀⠁⡀⠠⢐⢽⣻⡇⣯⣯⣞⡕⣽⡇⠨⠠⠁⠌⡐⠠⢁⠂⡂⢂⢐⠨⠠⢑⠐⡠⠨⢈⢐⠠⢁⠂⠄⠡⠨⢐⢝⠆⠌⠌⠌⡂⡺⣿⣿⣿⣷⡑⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡅⠂⠐⠌⠘⠀⠄⠀⠐⠠⡫⣗⣇⡿⡾⣽⢆⣟⡇⠌⠄⠅⠡⠠⢁⠂⠌⡐⢐⠐⠨⢐⢐⢁⠂⠌⡐⠠⠨⠠⢁⠂⠄⡁⠢⡹⡅⠅⠅⠅⡂⡺⣿⣿⣿⡷⡅⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢅⢂⠅⠅⡀⢁⠠⠀⠁⠈⠋⠢⠣⡫⡫⣪⢾⡽⡇⠨⠠⠁⠌⡐⠐⡈⡐⢐⠠⢁⢑⠐⡐⠠⠨⠐⠠⠡⠈⠌⡐⠀⠄⢂⠡⡹⡐⠡⡁⠅⡂⣺⣿⣿⣿⣟⢆⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠀⠂⡅⠠⠀⢀⠀⠂⠈⡀⠁⠐⢀⠐⡀⢂⢁⠑⡈⠄⡁⡂⢂⢁⢂⠐⡐⡈⡐⢐⠐⡈⡂⠅⡊⠌⠌⠌⡐⢀⠂⠐⡀⡂⢇⢇⢁⠂⠅⡂⣪⣿⣿⣿⣟⠆⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣁⠐⡌⡲⣈⢀⠀⠂⠀⠄⢀⠈⠀⡀⠄⠠⠀⡐⢀⠐⡀⢂⠐⠠⠐⡀⢂⠐⡐⠠⢁⠢⠠⢁⠂⠌⠄⠅⡂⡐⡈⡐⠠⠨⣺⢅⠂⠅⠅⡂⡺⣿⣿⣿⣯⠣⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⡳⡀⠕⢜⢮⢢⢣⢱⠀⠄⢄⢄⢁⠀⠄⠂⠂⠐⢀⠐⡀⢂⠨⠀⠅⡐⡀⠢⠠⢁⠂⠌⡐⡐⡈⡂⢅⣁⢢⣰⣄⢂⠡⢑⣽⢅⠊⠌⡐⡐⢼⣿⣿⣿⣯⠣⣻⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢕⢵⢱⠡⢱⡣⡣⡣⡣⡁⠀⡕⣵⣟⣟⢷⣕⢗⠁⠄⠂⡐⢀⠂⡁⡂⡐⠠⠡⢈⢐⠨⢐⢐⢀⢂⣴⣳⢣⠡⣳⣿⣷⢈⢢⠿⣅⢊⢔⠐⠄⣽⣻⣟⣿⡳⡕⡝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣵⢹⡪⣣⡃⠱⡕⡕⡕⡕⠅⠀⢪⣿⡽⡝⡝⡯⣗⠀⠂⡁⠄⠐⡀⠂⠄⠂⠌⠠⠡⢐⠐⡀⠢⢐⢸⣺⡪⢢⢣⣳⣿⢿⠠⡣⡃⠌⢌⢊⠊⢎⠪⢊⢊⠐⡀⡂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡲⣕⣝⢆⢊⢢⢃⠁⡁⠃⠇⢇⠅⠀⢕⡳⣿⣻⢾⣻⢵⠀⠁⠄⠂⢁⠀⠅⡈⠌⠠⠁⠌⡐⢐⠠⢑⢀⢢⢳⣱⣱⣵⣿⢿⡛⢌⢪⢂⢑⠐⠄⡑⡐⠨⢐⠀⠂⠠⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡐⢔⠸⡸⡐⢸⠰⡐⡀⠁⠀⠑⠑⠙⠪⢓⠣⡑⡀⠁⠂⢈⠀⡐⢀⠂⠌⠠⠁⠅⡐⡀⡂⠅⡐⡀⠓⠽⠾⠛⠝⡑⠄⡅⣧⢑⢐⢈⢲⣦⡢⢁⠂⠌⡨⠐⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡔⡜⡕⡑⠝⡜⡜⣕⢰⢸⡌⠨⢐⠐⠨⠀⠄⡀⠄⠠⠈⠠⠀⠂⠠⠐⢀⠁⢂⠁⡂⠄⠂⢄⠡⢐⠠⠡⢪⡴⣵⢵⢾⢽⣟⣿⡐⡐⡰⣘⢓⢇⠢⡈⡂⠄⣕⣼⣷⡢⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡰⡑⠅⠀⠀⠈⣺⡪⡎⣪⢮⢯⠈⣄⠌⠨⠠⢁⠐⡈⠄⡁⡊⠄⠡⠨⠠⠡⠨⢐⠨⢐⠡⡃⠕⢌⠢⠡⡱⠡⠡⠡⡑⠑⠕⡕⣟⢔⢔⢕⢬⢪⢪⠣⠐⣄⣿⣽⣿⣾⣧⢢⡱⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢌⠊⠀⠀⠀⢠⠪⡪⡪⢘⢗⡕⡁⣗⢽⡲⡦⣔⣄⣀⠂⠠⠐⡈⠄⠡⠨⠠⢁⠢⠨⢐⠨⠢⠡⡑⢨⠊⠢⢡⣡⡁⡂⠅⠡⡊⣮⢣⢯⡪⡇⡗⣭⢣⢓⠝⡙⢿⡿⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣄⢈⠠⠀⠀⠀⠀⡎⡊⡮⡊⠄⡇⡇⠄⢮⣳⣫⢯⣷⣻⣾⣻⣯⣧⡀⠈⠈⠀⠈⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⢀⢪⣲⢕⢨⠩⡇⡊⢮⡣⣣⡻⡐⡑⡜⡼⡰⡰⡸⠹⢋⢂⠱⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⡁⠀⢀⢾⢵⢷⡑⡀⠈⠀⡨⡪⡢⡳⡑⠠⡹⡪⠀⡳⡵⡽⣽⣾⣿⡾⡿⣯⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣕⢕⡇⡎⡮⣳⠨⡪⡺⣔⡕⡅⡌⢎⢯⠪⡃⠅⡑⢐⠄⠣⢑⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠠⠀⠁⢀⠠⠐⢝⣆⢱⠐⢐⠠⢠⢣⡳⡥⡳⡡⠁⢇⡇⠂⣝⢾⣽⣿⢯⡳⡝⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⡓⡇⣿⢪⢺⠐⢅⠫⢋⠏⢟⢝⢕⢆⠣⡱⠊⠌⡐⠨⠐⡀⠂⠌⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⠊⠀⠄⡰⣟⣯⡟⠷⡧⣆⣈⢜⢮⡺⣝⣮⣖⢭⡳⣙⣤⣯⣿⣿⡗⠓⢁⠀⡀⠠⠀⠠⠀⠂⠀⠄⠀⠄⠀⠄⠀⠄⠠⠐⠀⢀⢐⠐⡝⡔⢘⢕⠇⠅⠀⡀⠀⡨⢢⢣⠋⠁⢂⢐⠨⠐⢀⠂⠂⠄⠁⠌⠠⠈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡈⢀⠂⠘⢷⢦⠩⡊⢌⢙⢚⠿⡽⡻⣟⡿⣞⣿⣟⣾⣯⣿⠟⠋⡀⠁⠄⠠⠀⠄⠂⠠⠐⠀⠂⠀⠂⠀⠂⡀⠂⠠⠀⠄⠂⢀⢀⠐⡕⡅⠂⡇⠇⠀⠀⠀⢀⢪⢸⠐⠀⠀⡐⠠⠐⠈⠠⠐⠀⠌⠨⠈⠌⢄⠁⡂⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢸⢰⢘⢬⢨⢙⢿⣲⣔⡔⡐⢕⠹⢺⢩⣿⢿⣽⣟⠟⡋⠡⠈⠄⠂⡁⠐⡀⠂⠐⠀⠂⡀⠂⢈⠀⡁⢈⠠⠀⠂⢐⠀⢂⠈⠠⢀⠀⢇⠆⡀⡇⠁⠀⠀⠀⡐⠌⠂⠀⠀⠀⠄⠡⠈⠠⠁⠠⡁⠅⠡⡁⠅⡂⠅⠄⢅⢌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠃⠃⠇⠣⡳⡹⡻⢾⢶⣵⡵⣿⣻⠿⢋⠂⠅⢂⠡⠈⠄⡁⠄⠂⠐⠈⡀⠡⠐⠀⡈⢀⠠⠀⠄⠀⠂⡁⠄⠂⠐⢈⠠⠂⡠⡱⡁⣄⡢⡠⣄⢤⢄⠄⡐⠀⠀⠀⠠⠁⡂⠁⠌⠠⢁⠂⠅⡁⡂⢅⠢⠡⡑⢔⢕⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠁⡉⠘⠒⠕⠃⠅⠨⠠⢈⠐⡀⢂⠁⢂⠀⠂⡁⠈⠄⠀⠂⠐⠀⠄⠀⠄⠐⠀⡁⠂⠠⠐⠈⡈⠠⣈⢼⢼⢮⡟⡎⠫⠉⠊⠉⢫⢪⠂⠀⡀⠄⠨⠐⢀⠁⠅⡊⠄⠅⠅⡂⡂⢅⢊⢢⢪⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠁⠀⠁⡈⠀⠂⡀⠂⠐⠀⡈⠀⠄⠁⠀⠂⡀⢁⠈⠀⠂⡀⠁⠠⠈⠀⠄⠂⠁⡀⢁⢴⣺⣽⣻⢽⣳⡻⣀⢄⡠⣐⣀⠢⡑⠀⠁⠀⠀⠨⠐⠠⠈⠌⠄⠅⢕⠡⡂⢕⢰⠱⠑⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠠⠈⠀⠀⠠⠀⠈⠀⠄⠀⠀⡀⠈⠀⠀⠈⠀⡀⠁⡀⠐⠀⠄⠀⠫⢓⢟⠞⠟⠚⠝⠓⢋⠚⢕⢗⡕⡐⠀⢀⠀⠀⠌⠐⡈⠄⡑⠡⡑⢄⢕⠜⠜⠈⡀⠂⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠂⠀⠁⠨⡰⡰⡠⡡⡈⢀⠂⠄⢂⢁⠢⠁⠄⢀⠀⢀⠀⠅⠡⢐⠡⡨⡢⡪⠊⡈⠄⠂⡁⠠⠀⡁⠄⠀⠂⠁⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠀⠁⠑⠱⠜⢔⢄⠢⡀⡁⠠⠀⠠⠀⠄⡑⢅⢕⢌⠆⠣⠐⡀⠂⠄⡁⠄⠂⠁⢀⠠⠐⠀⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠑⠁⠡⠱⣐⠱⡘⠜⠈⠐⠈⡀⠁⠄⢈⠠⠀⡀⠂⠈⠀⠀⠀⡀⠀⠀⠐⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⠀⢀⠀⠀⠀⠠⠀⠂⠁⠀⠄⠈⠀⡀⠀⡀⠀⡀⠈⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀