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alsotang/24_game.json

Created February 21, 2024 11:51
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all solutions of 24 game
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24_game.json
{
"1,1,1,8": [
"(1+1+1)×8"
],
"1,1,1,11": [
"(11+1)×(1+1)"
],
"1,1,1,12": [
"(1+1)×12×1"
],
"1,1,1,13": [
"(13-1)×(1+1)"
],
"1,1,2,6": [
"(1+1)×6×2",
"(2+1+1)×6"
],
"1,1,2,7": [
"(7+1)×(2+1)"
],
"1,1,2,8": [
"(2+1)×8×1"
],
"1,1,2,9": [
"(9-1)×(2+1)"
],
"1,1,2,10": [
"(10+2)×(1+1)",
"(10+1+1)×2"
],
"1,1,2,11": [
"11×2+1+1",
"(1+1)×11+2",
"(11+1)×2×1"
],
"1,1,2,12": [
"12×2×1×1",
"12×2+1-1",
"12/(1-1/2)"
],
"1,1,2,13": [
"13×2-1-1",
"(1+1)×13-2",
"(13-1)×2×1"
],
"1,1,3,4": [
"(1+1)×4×3"
],
"1,1,3,5": [
"(5+1)×(3+1)"
],
"1,1,3,6": [
"(6+1+1)×3",
"(3+1)×6×1"
],
"1,1,3,7": [
"(7-1)×(3+1)",
"(7+1)×3×1"
],
"1,1,3,8": [
"8×3×1×1",
"8×3+1-1"
],
"1,1,3,9": [
"(9+3)×(1+1)",
"(9-1)×3×1"
],
"1,1,3,10": [
"(10-1-1)×3"
],
"1,1,3,11": [
"(11+1)×(3-1)"
],
"1,1,3,12": [
"(3-1)×12×1"
],
"1,1,3,13": [
"(13-1)×(3-1)"
],
"1,1,4,4": [
"(4+1+1)×4"
],
"1,1,4,5": [
"(4+1)×5-1",
"(5+1)×4×1"
],
"1,1,4,6": [
"6×4×1×1",
"6×4+1-1"
],
"1,1,4,7": [
"(7-1)×4×1",
"(7+1)×(4-1)"
],
"1,1,4,8": [
"(8+4)×(1+1)",
"(8-1-1)×4",
"(4-1)×8×1"
],
"1,1,4,9": [
"(9-1)×(4-1)"
],
"1,1,4,10": [
"(1+1)×10+4"
],
"1,1,4,12": [
"12×4/(1+1)",
"(4-1-1)×12"
],
"1,1,5,5": [
"(5+1)×(5-1)",
"(5×5-1)×1"
],
"1,1,5,6": [
"(5-1)×6×1",
"(6-1)×5-1"
],
"1,1,5,7": [
"(7+5)×(1+1)",
"(7-1)×(5-1)"
],
"1,1,5,8": [
"(5-1-1)×8"
],
"1,1,6,6": [
"(6+6)×(1+1)",
"(6-1-1)×6"
],
"1,1,6,8": [
"8×6/(1+1)"
],
"1,1,6,9": [
"(1+1)×9+6"
],
"1,1,6,12": [
"(1+1)×6+12"
],
"1,1,7,10": [
"(1+1)×7+10"
],
"1,1,8,8": [
"(1+1)×8+8"
],
"1,1,9,13": [
"13+9+1+1"
],
"1,1,10,12": [
"12+10+1+1"
],
"1,1,10,13": [
"(13+10+1)×1"
],
"1,1,11,11": [
"11+11+1+1"
],
"1,1,11,12": [
"(12+11+1)×1"
],
"1,1,11,13": [
"(13+11)×1×1",
"13+11+1-1"
],
"1,1,12,12": [
"(12+12)×1×1",
"12+12+1-1"
],
"1,1,12,13": [
"(13+12-1)×1"
],
"1,1,13,13": [
"13+13-1-1"
],
"1,2,2,4": [
"(2+1)×4×2"
],
"1,2,2,5": [
"(5+1)×(2+2)",
"(5+1)×2×2"
],
"1,2,2,6": [
"(6+2)×(2+1)",
"6×2×2×1",
"(2+2)×6×1"
],
"1,2,2,7": [
"(7-1)×(2+2)",
"(7-1)×2×2"
],
"1,2,2,8": [
"(2+2-1)×8",
"(2×2-1)×8"
],
"1,2,2,9": [
"(9+2+1)×2"
],
"1,2,2,10": [
"(10-2)×(2+1)",
"(10+2)×2×1",
"(10+1)×2+2"
],
"1,2,2,11": [
"(11+2-1)×2",
"(11×2+2)×1"
],
"1,2,2,12": [
"(2-1)×12×2",
"(12+1)×2-2",
"(12-1)×2+2",
"(2/2+1)×12"
],
"1,2,2,13": [
"(13+1-2)×2",
"(13×2-2)×1"
],
"1,2,3,3": [
"(3+1)×3×2"
],
"1,2,3,4": [
"(3+2+1)×4",
"4×3×2×1",
"(4+2)×(3+1)"
],
"1,2,3,5": [
"(5+3)×(2+1)",
"(5+2+1)×3",
"(5-1)×3×2",
"(3+2)×5-1"
],
"1,2,3,6": [
"(3+2-1)×6",
"(6+2)×3×1",
"(3-1)×6×2"
],
"1,2,3,7": [
"7×3+2+1",
"(2+1)×7+3",
"(7+2-1)×3"
],
"1,2,3,8": [
"(2-1)×8×3",
"(8-2)×(3+1)",
"(8+3+1)×2",
"8/(1-2/3)"
],
"1,2,3,9": [
"9×3-2-1",
"(2+1)×9-3",
"(9+3)×2×1",
"(9+1-2)×3"
],
"1,2,3,10": [
"10×2+3+1",
"(10-2)×3×1",
"(10+3-1)×2",
"(10+2)×(3-1)"
],
"1,2,3,11": [
"(11-3)×(2+1)",
"(11-2-1)×3",
"11×2+3-1",
"(3-1)×11+2"
],
"1,2,3,12": [
"(3+1-2)×12",
"(3+1)×12/2",
"12/(3/2-1)"
],
"1,2,3,13": [
"13×2+1-3",
"(3-1)×13-2"
],
"1,2,4,4": [
"(4+4)×(2+1)",
"(4+2)×4×1",
"(4-1)×4×2"
],
"1,2,4,5": [
"(5+2-1)×4",
"(4+2)×(5-1)"
],
"1,2,4,6": [
"(2-1)×6×4",
"(6+2)×(4-1)"
],
"1,2,4,7": [
"(7+1-2)×4",
"(7+4+1)×2"
],
"1,2,4,8": [
"(8+4)×2×1",
"(4+1-2)×8",
"(8-2)×4×1",
"(4/2+1)×8"
],
"1,2,4,9": [
"(9-2-1)×4",
"(9+4-1)×2",
"(9+1)×2+4"
],
"1,2,4,10": [
"(10-2)×(4-1)",
"(10×2+4)×1",
"(10/2+1)×4"
],
"1,2,4,11": [
"(11+1)×(4-2)",
"(11+1)×4/2",
"(11-1)×2+4"
],
"1,2,4,12": [
"(12-4)×(2+1)",
"(2+1)×4+12",
"12×4×1/2",
"(4-2)×12×1",
"12/(1-2/4)"
],
"1,2,4,13": [
"(13+1)×2-4",
"(13-1)×(4-2)",
"(13-1)×4/2"
],
"1,2,5,5": [
"5×5+1-2"
],
"1,2,5,6": [
"(5+1-2)×6",
"(5+1)×(6-2)",
"(6+5+1)×2"
],
"1,2,5,7": [
"(7+5)×2×1",
"(7+1)×(5-2)",
"(7-2)×5-1"
],
"1,2,5,8": [
"(5+1)×8/2",
"(8+5-1)×2",
"(8-2)×(5-1)",
"(5-2)×8×1"
],
"1,2,5,9": [
"(2+1)×5+9",
"9×2+5+1",
"(9-1)×(5-2)"
],
"1,2,5,10": [
"10×2+5-1",
"10×5/2-1"
],
"1,2,5,12": [
"(5-2-1)×12",
"(5+1)×2+12",
"(5-1)×12/2"
],
"1,2,5,13": [
"(13-5)×(2+1)",
"5×2+13+1"
],
"1,2,6,6": [
"(2+1)×6+6",
"(6+6)×2×1",
"(6-2)×6×1",
"(6/2+1)×6"
],
"1,2,6,7": [
"(7-2-1)×6",
"(7+6-1)×2",
"(7+1)×6/2",
"(7-1)×(6-2)"
],
"1,2,6,8": [
"(6-2-1)×8",
"8×6×1/2",
"(8+1)×2+6"
],
"1,2,6,9": [
"(9-1)×6/2",
"(9×2+6)×1"
],
"1,2,6,10": [
"(2+1)×10-6",
"(6+1)×2+10",
"(10-1)×2+6",
"(10/2-1)×6"
],
"1,2,6,11": [
"6×2+11+1"
],
"1,2,6,12": [
"12×6/(2+1)",
"(6×2+12)×1",
"(6/2-1)×12"
],
"1,2,6,13": [
"6×2+13-1"
],
"1,2,7,7": [
"(7×7-1)/2"
],
"1,2,7,8": [
"8×2+7+1",
"(7+1)×2+8",
"(7-1)×8/2"
],
"1,2,7,9": [
"9×2+7-1",
"7×2+9+1"
],
"1,2,7,10": [
"(7×2+10)×1"
],
"1,2,7,11": [
"7×2+11-1"
],
"1,2,7,12": [
"(7-1)×2+12"
],
"1,2,8,8": [
"(8×2+8)×1",
"(8/2-1)×8"
],
"1,2,8,9": [
"9×8/(2+1)",
"8×2+9-1",
"(9-1)×2+8"
],
"1,2,8,10": [
"(8-1)×2+10"
],
"1,2,8,13": [
"13+8+2+1"
],
"1,2,9,11": [
"(2+1)×11-9"
],
"1,2,9,12": [
"12+9+2+1"
],
"1,2,9,13": [
"(13+9+2)×1"
],
"1,2,10,11": [
"11+10+2+1"
],
"1,2,10,12": [
"(12+10+2)×1"
],
"1,2,10,13": [
"13+10+2-1"
],
"1,2,11,11": [
"(11+11+2)×1"
],
"1,2,11,12": [
"12+11+2-1",
"2/(1-11/12)"
],
"1,2,11,13": [
"(13+11)×(2-1)"
],
"1,2,12,12": [
"(2+1)×12-12",
"(12+12)×(2-1)"
],
"1,2,12,13": [
"13+12+1-2",
"2/(13/12-1)"
],
"1,2,13,13": [
"(13+13-2)×1"
],
"1,3,3,3": [
"(3+3)×(3+1)",
"(3×3-1)×3"
],
"1,3,3,4": [
"(4+3+1)×3",
"(3-1)×4×3",
"(3+3)×4×1"
],
"1,3,3,5": [
"(5+3)×3×1",
"(3+3)×(5-1)"
],
"1,3,3,6": [
"(6+3-1)×3",
"(6+1)×3+3"
],
"1,3,3,7": [
"(7×3+3)×1"
],
"1,3,3,8": [
"(8+1)×3-3",
"(8-1)×3+3"
],
"1,3,3,9": [
"(9-3)×(3+1)",
"(9+3)×(3-1)",
"(3-1/3)×9",
"(9×3-3)×1"
],
"1,3,3,10": [
"(10+1-3)×3",
"(10-1)×3-3"
],
"1,3,3,11": [
"(11-3)×3×1"
],
"1,3,3,12": [
"(3+1)×3+12",
"(12-3-1)×3",
"(3/3+1)×12"
],
"1,3,4,4": [
"(4+4)×3×1",
"(4+3-1)×4"
],
"1,3,4,5": [
"5×4+3+1",
"(3+1)×5+4",
"(5+4-1)×3",
"(5+3)×(4-1)"
],
"1,3,4,6": [
"6/(1-3/4)"
],
"1,3,4,7": [
"7×4-3-1",
"(3+1)×7-4",
"7×3+4-1",
"(4-1)×7+3"
],
"1,3,4,8": [
"(3+1)×4+8",
"(8+1-3)×4",
"(8+4)×(3-1)",
"8/(4/3-1)"
],
"1,3,4,9": [
"(4+1)×3+9",
"(9-3)×4×1",
"9×3+1-4",
"(4-1)×9-3"
],
"1,3,4,10": [
"(10-4)×(3+1)",
"(10-3-1)×4",
"(3-1)×10+4"
],
"1,3,4,11": [
"(11+1-4)×3",
"(11-3)×(4-1)",
"4×3+11+1"
],
"1,3,4,12": [
"(12-4)×3×1",
"(4+1-3)×12",
"12×4/(3-1)",
"(4×3+12)×1"
],
"1,3,4,13": [
"(13-4-1)×3",
"4×3+13-1"
],
"1,3,5,6": [
"6×3+5+1",
"(5+1)×3+6"
],
"1,3,5,7": [
"(7+5)×(3-1)",
"(5+1)×(7-3)"
],
"1,3,5,8": [
"(5+1-3)×8",
"5×3+8+1",
"(8-3)×5-1"
],
"1,3,5,9": [
"(9-3)×(5-1)",
"(5×3+9)×1",
"(5/3+1)×9"
],
"1,3,5,10": [
"10×3-5-1",
"5×3+10-1"
],
"1,3,5,11": [
"(11-5)×(3+1)",
"(11+1)×(5-3)"
],
"1,3,5,12": [
"(5+1)×12/3",
"(12+1-5)×3",
"(5-1)×3+12",
"(5-3)×12×1"
],
"1,3,5,13": [
"(13-5)×3×1",
"(13-1)×(5-3)"
],
"1,3,6,6": [
"(6+1-3)×6",
"(6+6)×(3-1)",
"(6×3+6)×1"
],
"1,3,6,7": [
"(7-3)×6×1",
"(7+1)×(6-3)",
"6×3+7-1",
"(7-1)×3+6"
],
"1,3,6,8": [
"(8-3-1)×6",
"8×6/(3-1)",
"(6-3)×8×1",
"(6/3+1)×8"
],
"1,3,6,9": [
"(3-1)×9+6",
"(6-1)×3+9",
"(9+1)×3-6",
"(9-1)×(6-3)",
"(9/3+1)×6"
],
"1,3,6,10": [
"(10×3-6)×1"
],
"1,3,6,11": [
"(11+1)×6/3",
"(11-1)×3-6"
],
"1,3,6,12": [
"(12-6)×(3+1)",
"(6-3-1)×12",
"12×6×1/3",
"(3-1)×6+12",
"12/(1-3/6)"
],
"1,3,6,13": [
"(13+1-6)×3",
"(13-1)×6/3"
],
"1,3,7,7": [
"(7-1)×(7-3)"
],
"1,3,7,8": [
"(7-3-1)×8",
"3/(1-7/8)"
],
"1,3,7,9": [
"(7+1)×9/3"
],
"1,3,7,10": [
"(3-1)×7+10",
"10×3+1-7"
],
"1,3,7,12": [
"(7-1)×12/3"
],
"1,3,7,13": [
"13+7+3+1",
"(13-7)×(3+1)"
],
"1,3,8,8": [
"(3+1)×8-8",
"(3-1)×8+8",
"(8+1)×8/3"
],
"1,3,8,9": [
"9×8×1/3",
"3/(9/8-1)"
],
"1,3,8,10": [
"(10-1)×8/3"
],
"1,3,8,11": [
"11×3-8-1"
],
"1,3,8,12": [
"12+8+3+1",
"12×8/(3+1)",
"(12/3-1)×8"
],
"1,3,8,13": [
"(13+8+3)×1"
],
"1,3,9,9": [
"(9-1)×9/3"
],
"1,3,9,10": [
"(10+1)×3-9"
],
"1,3,9,11": [
"11+9+3+1",
"(11×3-9)×1",
"(11/3-1)×9"
],
"1,3,9,12": [
"(3+1)×9-12",
"(12-1)×3-9",
"(12+9+3)×1",
"(9/3-1)×12"
],
"1,3,9,13": [
"13+9+3-1"
],
"1,3,10,10": [
"10+10+3+1"
],
"1,3,10,11": [
"11×3+1-10",
"(11+10+3)×1"
],
"1,3,10,12": [
"12+10+3-1"
],
"1,3,11,11": [
"11+11+3-1"
],
"1,3,11,12": [
"12×3-11-1",
"(11+1)×3-12"
],
"1,3,12,12": [
"(12×3-12)×1"
],
"1,3,12,13": [
"12×3+1-13",
"(13-1)×3-12"
],
"1,3,13,13": [
"13+13+1-3"
],
"1,4,4,4": [
"(4+1)×4+4",
"(4+4)×(4-1)"
],
"1,4,4,5": [
"(5×4+4)×1"
],
"1,4,4,6": [
"(6+1)×4-4",
"(6-1)×4+4"
],
"1,4,4,7": [
"4×4+7+1",
"(7×4-4)×1"
],
"1,4,4,8": [
"(8-1)×4-4",
"(4×4+8)×1"
],
"1,4,4,9": [
"(9+1-4)×4",
"4×4+9-1"
],
"1,4,4,10": [
"(10-4)×4×1"
],
"1,4,4,11": [
"(11-4-1)×4"
],
"1,4,4,12": [
"(12-4)×(4-1)",
"(4-1)×4+12",
"(4/4+1)×12"
],
"1,4,5,5": [
"5×4+5-1",
"(5-1)×5+4"
],
"1,4,5,6": [
"6/(5/4-1)",
"4/(1-5/6)"
],
"1,4,5,7": [
"7×4+1-5",
"(5-1)×7-4"
],
"1,4,5,8": [
"(5+1)×(8-4)",
"(5-1)×4+8"
],
"1,4,5,9": [
"(4-1)×5+9",
"(9-4)×5-1"
],
"1,4,5,10": [
"(10+1-5)×4",
"(10-4)×(5-1)"
],
"1,4,5,11": [
"(11-5)×4×1"
],
"1,4,5,12": [
"(5+1-4)×12",
"(12-5-1)×4"
],
"1,4,5,13": [
"(13-5)×(4-1)"
],
"1,4,6,6": [
"(4+1)×6-6",
"(4-1)×6+6"
],
"1,4,6,7": [
"(7+1-4)×6",
"4/(7/6-1)"
],
"1,4,6,8": [
"(6+1-4)×8",
"(8-4)×6×1",
"8/(1-4/6)"
],
"1,4,6,9": [
"(9-4-1)×6"
],
"1,4,6,10": [
"(4-1)×10-6"
],
"1,4,6,11": [
"(11+1-6)×4",
"(11+1)×(6-4)"
],
"1,4,6,12": [
"(12-6)×4×1",
"12×6/(4-1)",
"(6-4)×12×1",
"12/(6/4-1)",
"(12/4+1)×6"
],
"1,4,6,13": [
"13+6+4+1",
"(13-6-1)×4",
"(13-1)×(6-4)"
],
"1,4,7,7": [
"(7+1)×(7-4)"
],
"1,4,7,8": [
"8×4-7-1",
"(7+1)×4-8",
"(7-1)×(8-4)",
"(7-4)×8×1"
],
"1,4,7,9": [
"(9-1)×(7-4)"
],
"1,4,7,11": [
"(4+1)×7-11"
],
"1,4,7,12": [
"12+7+4+1",
"(7-4-1)×12",
"(7+1)×12/4",
"(12+1-7)×4"
],
"1,4,7,13": [
"(13-7)×4×1",
"(13+7+4)×1"
],
"1,4,8,8": [
"(8-4-1)×8",
"(8×4-8)×1",
"(8/4+1)×8"
],
"1,4,8,9": [
"9×8/(4-1)",
"8×4+1-9",
"(9-1)×4-8"
],
"1,4,8,11": [
"11+8+4+1",
"(11+1)×8/4"
],
"1,4,8,12": [
"12×8×1/4",
"(8+1)×4-12",
"(12+8+4)×1",
"12/(1-4/8)"
],
"1,4,8,13": [
"13+8+4-1",
"(13+1-8)×4",
"(13-1)×8/4"
],
"1,4,9,10": [
"10+9+4+1"
],
"1,4,9,11": [
"(4-1)×11-9",
"9×4-11-1",
"(11+9+4)×1"
],
"1,4,9,12": [
"12+9+4-1",
"(9-1)×12/4",
"(9×4-12)×1"
],
"1,4,9,13": [
"9×4+1-13"
],
"1,4,10,10": [
"(10+10+4)×1",
"10×10/4-1"
],
"1,4,10,11": [
"11+10+4-1"
],
"1,4,10,12": [
"12×10/(4+1)",
"(10-1)×4-12",
"4/(1-10/12)"
],
"1,4,12,12": [
"(4-1)×12-12",
"(12/4-1)×12"
],
"1,5,5,5": [
"(5-1/5)×5"
],
"1,5,5,6": [
"6×5-5-1",
"(5+1)×5-6"
],
"1,5,5,9": [
"(5+1)×(9-5)"
],
"1,5,5,10": [
"(10-5)×5-1"
],
"1,5,5,11": [
"(11-5)×(5-1)"
],
"1,5,5,12": [
"(5/5+1)×12"
],
"1,5,5,13": [
"13+5+5+1"
],
"1,5,6,6": [
"(6×5-6)×1"
],
"1,5,6,7": [
"6×5+1-7",
"(7-1)×5-6"
],
"1,5,6,8": [
"(8+1-5)×6"
],
"1,5,6,9": [
"(9-5)×6×1"
],
"1,5,6,10": [
"(5+1)×(10-6)",
"(10-5-1)×6"
],
"1,5,6,11": [
"(6+1)×5-11",
"(11-6)×5-1"
],
"1,5,6,12": [
"12+6+5+1",
"(5+1)×6-12",
"(6+1-5)×12",
"(12-6)×(5-1)"
],
"1,5,6,13": [
"(13+6+5)×1"
],
"1,5,7,8": [
"(7+1-5)×8",
"(7+1)×(8-5)"
],
"1,5,7,9": [
"(7-1)×(9-5)"
],
"1,5,7,10": [
"7×5-10-1",
"(7/5+1)×10"
],
"1,5,7,11": [
"11+7+5+1",
"(5+1)×(11-7)",
"(11+1)×(7-5)",
"(7×5-11)×1"
],
"1,5,7,12": [
"(7-5)×12×1",
"7×5+1-12",
"(12+7+5)×1",
"(12-7)×5-1"
],
"1,5,7,13": [
"13+7+5-1",
"(13-7)×(5-1)",
"(13-1)×(7-5)"
],
"1,5,8,8": [
"(5-1)×8-8",
"(8-5)×8×1"
],
"1,5,8,9": [
"(9-5-1)×8",
"(9-1)×(8-5)",
"9/(1-5/8)"
],
"1,5,8,10": [
"10+8+5+1",
"(10/5+1)×8"
],
"1,5,8,11": [
"(8-1)×5-11",
"(11+8+5)×1"
],
"1,5,8,12": [
"(5+1)×(12-8)",
"(8-5-1)×12",
"12+8+5-1",
"12×8/(5-1)"
],
"1,5,8,13": [
"(13-8)×5-1"
],
"1,5,9,9": [
"9+9+5+1"
],
"1,5,9,10": [
"(10+9+5)×1"
],
"1,5,9,11": [
"11+9+5-1"
],
"1,5,9,12": [
"(5-1)×9-12",
"(9+1)×12/5"
],
"1,5,9,13": [
"(5+1)×(13-9)"
],
"1,5,10,10": [
"10+10+5-1"
],
"1,5,10,11": [
"(11+1)×10/5"
],
"1,5,10,12": [
"12×10×1/5",
"12/(1-5/10)"
],
"1,5,10,13": [
"(13-1)×10/5"
],
"1,5,11,11": [
"(11×11-1)/5"
],
"1,5,11,12": [
"(11-1)×12/5"
],
"1,5,12,12": [
"12×12/(5+1)"
],
"1,6,6,6": [
"(6-1)×6-6"
],
"1,6,6,8": [
"6/(1-6/8)"
],
"1,6,6,9": [
"(9+1-6)×6"
],
"1,6,6,10": [
"(10-6)×6×1"
],
"1,6,6,11": [
"11+6+6+1",
"(11-6-1)×6",
"6×6-11-1"
],
"1,6,6,12": [
"(12+6+6)×1",
"(6×6-12)×1",
"(6/6+1)×12"
],
"1,6,6,13": [
"13+6+6-1",
"6×6+1-13"
],
"1,6,7,9": [
"(7+1)×(9-6)"
],
"1,6,7,10": [
"10+7+6+1",
"(10+1-7)×6",
"(7-1)×(10-6)"
],
"1,6,7,11": [
"(11-7)×6×1",
"(6-1)×7-11",
"(11+7+6)×1"
],
"1,6,7,12": [
"12+7+6-1",
"(7+1-6)×12",
"(12-7-1)×6",
"(7-1)×6-12"
],
"1,6,8,8": [
"(8+1-6)×8",
"8/(8/6-1)"
],
"1,6,8,9": [
"9+8+6+1",
"(9-6)×8×1",
"8/(1-6/9)"
],
"1,6,8,10": [
"(10-6-1)×8",
"(10+8+6)×1",
"6/(10/8-1)"
],
"1,6,8,11": [
"11+8+6-1",
"(11+1-8)×6",
"(11+1)×(8-6)"
],
"1,6,8,12": [
"(12-8)×6×1",
"(8-6)×12×1",
"(12/6+1)×8"
],
"1,6,8,13": [
"(13-8-1)×6",
"(13-1)×(8-6)"
],
"1,6,9,9": [
"(9-1)×(9-6)",
"(9+9+6)×1"
],
"1,6,9,10": [
"10+9+6-1",
"(10/6+1)×9"
],
"1,6,9,12": [
"(9-6-1)×12",
"(12+1-9)×6",
"12/(9/6-1)",
"6/(1-9/12)"
],
"1,6,9,13": [
"(13-9)×6×1"
],
"1,6,10,12": [
"12×10/(6-1)"
],
"1,6,10,13": [
"(13+1-10)×6"
],
"1,6,11,12": [
"(11+1)×12/6"
],
"1,6,11,13": [
"(13×11+1)/6"
],
"1,6,12,12": [
"12×12×1/6",
"12/(1-6/12)"
],
"1,6,12,13": [
"(13-1)×12/6"
],
"1,7,7,9": [
"9+7+7+1"
],
"1,7,7,10": [
"(7+1)×(10-7)",
"(10+7+7)×1"
],
"1,7,7,11": [
"11+7+7-1",
"(7-1)×(11-7)"
],
"1,7,7,12": [
"(7/7+1)×12"
],
"1,7,8,8": [
"8+8+7+1"
],
"1,7,8,9": [
"(9+1-7)×8",
"(9+8+7)×1"
],
"1,7,8,10": [
"10+8+7-1",
"(10-7)×8×1"
],
"1,7,8,11": [
"(7+1)×(11-8)",
"(11-7-1)×8"
],
"1,7,8,12": [
"(8+1-7)×12",
"(7-1)×(12-8)"
],
"1,7,9,9": [
"9+9+7-1"
],
"1,7,9,10": [
"(9-1)×(10-7)"
],
"1,7,9,11": [
"(11+1)×(9-7)"
],
"1,7,9,12": [
"(7+1)×(12-9)",
"(9-7)×12×1"
],
"1,7,9,13": [
"(7-1)×(13-9)",
"(13-1)×(9-7)"
],
"1,7,10,12": [
"(10-7-1)×12",
"10/(1-7/12)"
],
"1,7,10,13": [
"(7+1)×(13-10)"
],
"1,7,12,12": [
"12×12/(7-1)"
],
"1,7,12,13": [
"(13+1)×12/7"
],
"1,7,13,13": [
"(13×13-1)/7"
],
"1,8,8,8": [
"(8+8+8)×1"
],
"1,8,8,9": [
"9+8+8-1"
],
"1,8,8,10": [
"(10+1-8)×8"
],
"1,8,8,11": [
"(11-8)×8×1"
],
"1,8,8,12": [
"(12-8-1)×8",
"(8/8+1)×12",
"8/(1-8/12)"
],
"1,8,9,11": [
"(11+1-9)×8",
"(9-1)×(11-8)",
"9/(11/8-1)"
],
"1,8,9,12": [
"(12-9)×8×1",
"(9+1-8)×12",
"8/(12/9-1)"
],
"1,8,9,13": [
"(13-9-1)×8"
],
"1,8,10,11": [
"(11+1)×(10-8)"
],
"1,8,10,12": [
"(12+1-10)×8",
"(10-8)×12×1"
],
"1,8,10,13": [
"(13-10)×8×1",
"(13-1)×(10-8)"
],
"1,8,11,12": [
"(11-8-1)×12"
],
"1,8,11,13": [
"(13+1-11)×8"
],
"1,8,12,12": [
"12/(12/8-1)"
],
"1,9,9,12": [
"(9-1)×(12-9)",
"(9/9+1)×12"
],
"1,9,10,12": [
"(10+1-9)×12"
],
"1,9,10,13": [
"(9-1)×(13-10)"
],
"1,9,11,11": [
"(11+1)×(11-9)"
],
"1,9,11,12": [
"(11-9)×12×1"
],
"1,9,11,13": [
"(13-1)×(11-9)"
],
"1,9,12,12": [
"(12-9-1)×12"
],
"1,10,10,12": [
"(10/10+1)×12"
],
"1,10,11,12": [
"(11+1-10)×12",
"(11+1)×(12-10)"
],
"1,10,12,12": [
"(12-10)×12×1"
],
"1,10,12,13": [
"(13-10-1)×12",
"(13-1)×(12-10)"
],
"1,11,11,12": [
"(11/11+1)×12"
],
"1,11,11,13": [
"(11+1)×(13-11)",
"(13/11+1)×11"
],
"1,11,12,12": [
"(12+1-11)×12"
],
"1,11,12,13": [
"(13-11)×12×1"
],
"1,11,13,13": [
"(13-1)×(13-11)",
"(11/13+1)×13"
],
"1,12,12,12": [
"(12/12+1)×12"
],
"1,12,12,13": [
"(13+1-12)×12"
],
"1,12,13,13": [
"(13/13+1)×12"
],
"2,2,2,3": [
"(2+2)×3×2",
"3×2×2×2"
],
"2,2,2,4": [
"(4+2)×(2+2)",
"(2+2+2)×4",
"(4+2)×2×2",
"(2×2+2)×4"
],
"2,2,2,5": [
"(5×2+2)×2"
],
"2,2,2,7": [
"(7×2-2)×2"
],
"2,2,2,8": [
"(8-2)×(2+2)",
"(8+2+2)×2",
"(8-2)×2×2",
"(2×2+8)×2",
"(2/2+2)×8"
],
"2,2,2,9": [
"(9+2)×2+2"
],
"2,2,2,10": [
"10×2+2+2",
"10×2+2×2"
],
"2,2,2,11": [
"(2/2+11)×2",
"(11+2)×2-2"
],
"2,2,2,12": [
"(2+2)×12/2",
"12×2×2/2",
"(2×2-2)×12",
"12×2+2-2"
],
"2,2,2,13": [
"(13-2/2)×2",
"(13-2)×2+2"
],
"2,2,3,3": [
"(3+3)×(2+2)",
"(3+3)×2×2",
"(3×2+2)×3"
],
"2,2,3,4": [
"(4+2+2)×3",
"(2×2+4)×3"
],
"2,2,3,5": [
"(5×2-2)×3"
],
"2,2,3,6": [
"(2/2+3)×6",
"(6-2)×3×2",
"(3×2-2)×6",
"(3×2+6)×2"
],
"2,2,3,7": [
"(2/2+7)×3",
"(7+3+2)×2"
],
"2,2,3,8": [
"8×3+2-2",
"8×3×2/2",
"(8+3)×2+2"
],
"2,2,3,9": [
"(9-3)×(2+2)",
"(9-3)×2×2",
"(9-2/2)×3",
"9×2+3×2",
"(2/3+2)×9"
],
"2,2,3,10": [
"(10+3)×2-2"
],
"2,2,3,11": [
"(11+3-2)×2"
],
"2,2,3,12": [
"(2+2)×3+12",
"(12-2-2)×3",
"3×2×2+12",
"(12-2×2)×3",
"(3-2/2)×12",
"(3-2)×12×2",
"12/(2-3/2)",
"(12/2+2)×3"
],
"2,2,3,13": [
"(13+2-3)×2"
],
"2,2,4,4": [
"(4×2-2)×4",
"(4×2+4)×2"
],
"2,2,4,5": [
"5×4+2+2",
"(2+2)×5+4",
"5×4+2×2",
"5×2×2+4",
"(2/2+5)×4",
"(5-2)×4×2"
],
"2,2,4,6": [
"6×4+2-2",
"6×4×2/2",
"(4+2)×(6-2)",
"(6+4+2)×2",
"(4-2)×6×2",
"(4/2+2)×6"
],
"2,2,4,7": [
"7×4-2-2",
"(2+2)×7-4",
"7×4-2×2",
"7×2×2-4",
"(7-2/2)×4",
"(7+4)×2+2"
],
"2,2,4,8": [
"(2+2)×4+8",
"4×2×2+8",
"(4-2/2)×8",
"(4+2)×8/2",
"8×2+4×2",
"(8+2)×2+4",
"(8×2-4)×2",
"(8/2+2)×4"
],
"2,2,4,9": [
"9×2+4+2",
"(9+4)×2-2"
],
"2,2,4,10": [
"(10-4)×(2+2)",
"(10-2-2)×4",
"(10-4)×2×2",
"(10-2×2)×4",
"(10+4-2)×2",
"(10+2)×(4-2)",
"(10+2)×4/2",
"(4/2+10)×2"
],
"2,2,4,11": [
"11×2+4-2",
"(4-2)×11+2",
"11×4/2+2",
"11×2+4/2"
],
"2,2,4,12": [
"(4+2)×2+12",
"(12+2)×2-4",
"(12-2)×2+4"
],
"2,2,4,13": [
"13×2+2-4",
"(4-2)×13-2",
"13×4/2-2",
"13×2-4/2"
],
"2,2,5,5": [
"5×5-2/2",
"(5+5+2)×2"
],
"2,2,5,6": [
"(5-2/2)×6",
"(6+2)×(5-2)",
"(6+5)×2+2"
],
"2,2,5,7": [
"7×2+5×2"
],
"2,2,5,8": [
"(8+5)×2-2"
],
"2,2,5,9": [
"(9+5-2)×2"
],
"2,2,5,10": [
"(5+2)×2+10",
"(10-2)×(5-2)",
"(2/5+2)×10",
"(10×5-2)/2"
],
"2,2,5,11": [
"(11-5)×(2+2)",
"(11-5)×2×2"
],
"2,2,5,12": [
"5×2+12+2",
"12/(5/2-2)"
],
"2,2,6,6": [
"(6+2)×6/2",
"6×2+6×2"
],
"2,2,6,7": [
"(7+2)×2+6",
"(7+6)×2-2"
],
"2,2,6,8": [
"(8-2-2)×6",
"(8-2×2)×6",
"8×2+6+2",
"(6+2)×2+8",
"(8+6-2)×2",
"(8-2)×(6-2)"
],
"2,2,6,9": [
"(6/2+9)×2",
"(9×2-6)×2"
],
"2,2,6,10": [
"6×2+10+2",
"10×2+6-2",
"(10-2)×6/2"
],
"2,2,6,11": [
"(11-2)×2+6"
],
"2,2,6,12": [
"(12-6)×(2+2)",
"(6-2-2)×12",
"(12-6)×2×2",
"(6-2×2)×12",
"(6-2)×12/2",
"(12/2-2)×6",
"(12/2+6)×2"
],
"2,2,6,13": [
"(13+2)×2-6"
],
"2,2,7,7": [
"(7+7-2)×2"
],
"2,2,7,8": [
"(7-2-2)×8",
"(7-2×2)×8",
"7×2+8+2"
],
"2,2,7,10": [
"(10/2+7)×2"
],
"2,2,7,12": [
"7×2+12-2"
],
"2,2,7,13": [
"13+7+2+2",
"(13-7)×(2+2)",
"2×2+13+7",
"(13-7)×2×2"
],
"2,2,8,8": [
"(2+2)×8-8",
"8×2×2-8",
"(8-2)×8/2",
"(8/2+8)×2"
],
"2,2,8,9": [
"9×2+8-2"
],
"2,2,8,10": [
"8×2+10-2",
"10×2+8/2",
"(10×2-8)×2",
"(10-2)×2+8",
"(10/2-2)×8"
],
"2,2,8,12": [
"12+8+2+2",
"12×8/(2+2)",
"2×2+12+8",
"12×8/2/2",
"(8-2)×2+12",
"(8/2-2)×12"
],
"2,2,9,10": [
"(9-2)×2+10"
],
"2,2,9,11": [
"11+9+2+2",
"2×2+11+9"
],
"2,2,9,12": [
"(2+2)×9-12",
"9×2×2-12",
"9×2+12/2"
],
"2,2,10,10": [
"10+10+2+2",
"2×2+10+10"
],
"2,2,10,11": [
"(11×2-10)×2"
],
"2,2,10,13": [
"2/2+13+10"
],
"2,2,11,11": [
"(2/11+2)×11"
],
"2,2,11,12": [
"2/2+12+11"
],
"2,2,11,13": [
"13+11+2-2",
"(13+11)×2/2"
],
"2,2,12,12": [
"12+12+2-2",
"(12+12)×2/2",
"(12×2-12)×2"
],
"2,2,12,13": [
"13+12-2/2"
],
"2,2,13,13": [
"(2-2/13)×13"
],
"2,3,3,3": [
"(3+3+2)×3",
"(3×3+3)×2"
],
"2,3,3,5": [
"(5+2)×3+3",
"(5×3-3)×2"
],
"2,3,3,6": [
"6×3+3×2",
"3×3×2+6",
"(3+3-2)×6",
"(3+3)×(6-2)",
"(6+3+3)×2"
],
"2,3,3,7": [
"(7-3)×3×2",
"(7+3-2)×3",
"(7+2)×3-3"
],
"2,3,3,8": [
"(3×2-3)×8",
"(3-2)×8×3",
"(3+3)×8/2",
"(3/3+2)×8"
],
"2,3,3,9": [
"(3+2)×3+9",
"(9+2-3)×3",
"9×2+3+3",
"(9-2)×3+3"
],
"2,3,3,10": [
"10×3-3×2",
"(10/2+3)×3"
],
"2,3,3,11": [
"(11-2)×3-3",
"(3/3+11)×2"
],
"2,3,3,12": [
"12×3×2/3",
"12×2+3-3",
"(3+3)×2+12"
],
"2,3,3,13": [
"(13-3-2)×3",
"(13+3)×3/2",
"3×3+13+2",
"(13-3/3)×2"
],
"2,3,4,4": [
"(3+2)×4+4",
"4×4×3/2",
"(4-2)×4×3"
],
"2,3,4,5": [
"(5+3-2)×4",
"(5+4+3)×2"
],
"2,3,4,6": [
"(3-2)×6×4",
"6×3+4+2",
"(4+2)×3+6",
"(6-3)×4×2",
"(6+4-2)×3",
"(4/2+6)×3",
"6×2+4×3",
"(6×2-4)×3",
"(6/2+3)×4"
],
"2,3,4,7": [
"(7+2-3)×4",
"(4+2)×(7-3)",
"(7+3)×2+4"
],
"2,3,4,8": [
"(8-4)×3×2",
"(4+2-3)×8",
"(8/2+4)×3"
],
"2,3,4,9": [
"9×4×2/3",
"(9+3)×(4-2)",
"(9+3)×4/2"
],
"2,3,4,10": [
"10×3-4-2",
"(10+2-4)×3",
"(10-4/2)×3",
"4×3+10+2",
"(4+3)×2+10"
],
"2,3,4,11": [
"(11-3-2)×4",
"(11+4-3)×2",
"(11+3)×2-4"
],
"2,3,4,12": [
"(3×2-4)×12",
"(12-3×2)×4",
"(12+4)×3/2",
"(4+2)×12/3",
"(4-3)×12×2",
"(12/3+2)×4"
],
"2,3,4,13": [
"4×2+13+3",
"(13+3-4)×2",
"(13-3)×2+4"
],
"2,3,5,5": [
"5×5+2-3",
"(5+5-2)×3",
"(5+3)×(5-2)"
],
"2,3,5,6": [
"6×5-3×2",
"5×3×2-6",
"(5+2-3)×6",
"(5-3)×6×2",
"(5+3)×6/2",
"(6/2+5)×3"
],
"2,3,5,7": [
"7×3+5-2",
"(5-2)×7+3",
"5×3+7+2"
],
"2,3,5,8": [
"8×2+5+3",
"(5+3)×2+8",
"8/(2-5/3)"
],
"2,3,5,9": [
"(9-5)×3×2",
"9×3+2-5",
"(5-2)×9-3",
"(9×5+3)/2"
],
"2,3,5,10": [
"(10+2)×(5-3)",
"(10+5-3)×2"
],
"2,3,5,11": [
"(11+5)×3/2",
"5×2+11+3",
"(11+2-5)×3",
"(11-3)×(5-2)",
"11×2+5-3",
"5×3+11-2",
"(5-3)×11+2"
],
"2,3,5,12": [
"12/(3-5/2)"
],
"2,3,5,13": [
"3×2+13+5",
"13×2+3-5",
"(5-3)×13-2"
],
"2,3,6,6": [
"(3+2)×6-6",
"6×6×2/3",
"(6+2)×(6-3)",
"(6+3)×2+6",
"(6×3-6)×2",
"(6/3+2)×6"
],
"2,3,6,7": [
"7×6/2+3",
"7×3+6/2",
"(7×2-6)×3"
],
"2,3,6,8": [
"(8+2)×3-6",
"6×3+8-2",
"(8-2)×3+6"
],
"2,3,6,9": [
"(9-3-2)×6",
"(6+2)×9/3",
"6×2+9+3",
"(9-3)×(6-2)",
"(3-2/6)×9",
"9×6/2-3",
"9×3-6/2",
"(9+6-3)×2"
],
"2,3,6,10": [
"(10-6)×3×2",
"(10-3×2)×6",
"(10+6)×3/2",
"(10+2)×6/3",
"(10-2)×(6-3)",
"(6/3+10)×2"
],
"2,3,6,11": [
"(11-3)×6/2",
"(11-6/2)×3",
"11×2+6/3",
"11×6/3+2"
],
"2,3,6,12": [
"3×2+12+6",
"6×3×2-12",
"12×3/2+6",
"12×3-6×2",
"(12+2-6)×3",
"(6-2)×3+12",
"(12-2)×3-6",
"6×3+12/2",
"(12+3)×2-6",
"(12-3)×2+6"
],
"2,3,6,13": [
"13+6+3+2",
"13×2-6/3",
"13×6/3-2"
],
"2,3,7,7": [
"7×2+7+3"
],
"2,3,7,8": [
"(7+2)×8/3",
"(8-2)×(7-3)",
"(8+7-3)×2",
"8/(7/3-2)"
],
"2,3,7,9": [
"(9+7)×3/2",
"(7-2)×3+9",
"(7×3-9)×2"
],
"2,3,7,10": [
"10×2+7-3",
"(10×7+2)/3"
],
"2,3,7,11": [
"(3+2)×7-11",
"3×2+11+7",
"(11-7)×3×2",
"11×3-7-2"
],
"2,3,7,12": [
"12+7+3+2",
"(7-3-2)×12",
"12/(7/2-3)",
"(7-3)×12/2"
],
"2,3,7,13": [
"7×2+13-3",
"(13+2-7)×3"
],
"2,3,8,8": [
"(8-3-2)×8",
"(8+8)×3/2",
"(8×2-8)×3"
],
"2,3,8,9": [
"(9-3×2)×8",
"(9-3)×8/2"
],
"2,3,8,10": [
"3×2+10+8",
"10×3+2-8"
],
"2,3,8,11": [
"11+8+3+2",
"8×2+11-3",
"(11-2)×8/3",
"(11-3)×2+8"
],
"2,3,8,12": [
"(12-8)×3×2",
"(8-3×2)×12",
"8×3/2+12",
"(8-2)×12/3",
"(12-8/2)×3",
"(12/2-3)×8",
"(8×3-12)×2",
"(12/3+8)×2"
],
"2,3,8,13": [
"(13+3)×2-8"
],
"2,3,9,9": [
"3×2+9+9",
"(9+2)×3-9",
"9×2+9-3",
"(9/3+9)×2"
],
"2,3,9,10": [
"10+9+3+2",
"10×3/2+9",
"(9×2-10)×3",
"(10-2)×9/3"
],
"2,3,9,12": [
"(9-3)×2+12"
],
"2,3,9,13": [
"(13-9)×3×2",
"(13-2)×3-9",
"(13×3+9)/2"
],
"2,3,10,10": [
"(10-3)×2+10"
],
"2,3,10,12": [
"12×10/(3+2)",
"12×3-10-2",
"(10+2)×3-12",
"10×2+12/3",
"(10×2-12)×3",
"(10/2-3)×12",
"10×3-12/2"
],
"2,3,10,13": [
"13+10+3-2",
"(13-10/2)×3"
],
"2,3,11,11": [
"11×3+2-11"
],
"2,3,11,12": [
"12+11+3-2"
],
"2,3,11,13": [
"(13+11)×(3-2)"
],
"2,3,12,12": [
"12×12/3/2",
"(12+12)×(3-2)",
"(12×3+12)/2",
"(12/3-2)×12"
],
"2,3,12,13": [
"13+12+2-3"
],
"2,3,13,13": [
"13×3-13-2"
],
"2,4,4,4": [
"4×4+4×2",
"(4+4-2)×4",
"(4/2+4)×4",
"(4+4+4)×2",
"(4×4-4)×2"
],
"2,4,4,5": [
"(5+2)×4-4",
"(5×2-4)×4",
"(4+4)×(5-2)"
],
"2,4,4,6": [
"(4×2-4)×6",
"4×4+6+2",
"(4+4)×6/2",
"(6+4)×2+4"
],
"2,4,4,7": [
"(7-4)×4×2",
"(7-2)×4+4"
],
"2,4,4,8": [
"(4+2)×(8-4)",
"8×4-4×2",
"4×4×2-8",
"(8+2-4)×4",
"(8+4)×(4-2)",
"(8+4)×4/2",
"(8-4/2)×4",
"8×2+4+4",
"(4+4)×2+8",
"(4/4+2)×8"
],
"2,4,4,9": [
"(9-2)×4-4"
],
"2,4,4,10": [
"(4-2)×10+4",
"10×4/2+4",
"4×4+10-2",
"(10+4)×2-4"
],
"2,4,4,11": [
"(4/4+11)×2",
"(11×4+4)/2"
],
"2,4,4,12": [
"(12-4-2)×4",
"4×2+12+4",
"12×4×2/4",
"12×4/(4-2)",
"(4-4/2)×12",
"12×2+4-4"
],
"2,4,4,13": [
"(13-4/4)×2",
"(13×4-4)/2"
],
"2,4,5,5": [
"(5+5)×2+4"
],
"2,4,5,6": [
"6×5-4-2",
"(4+2)×5-6",
"5×4+6-2",
"(6-2)×5+4",
"(5+4)×2+6"
],
"2,4,5,7": [
"(7+5)×(4-2)",
"(7+5)×4/2"
],
"2,4,5,8": [
"(8-5)×4×2",
"(4×2-5)×8",
"(5+2-4)×8",
"(5-4/2)×8",
"8×5/2+4",
"5×4+8/2",
"(5×4-8)×2"
],
"2,4,5,9": [
"(4+2)×(9-5)",
"(9+2-5)×4",
"(9+5)×2-4"
],
"2,4,5,10": [
"5×2+10+4"
],
"2,4,5,11": [
"4×2+11+5",
"(11+5-4)×2"
],
"2,4,5,12": [
"(12-4)×(5-2)",
"(5-2)×4+12",
"(5-4)×12×2"
],
"2,4,5,13": [
"13+5+4+2",
"(13-5-2)×4",
"(13+4-5)×2"
],
"2,4,6,6": [
"(6+2-4)×6",
"(6+6)×(4-2)",
"(6+6)×4/2",
"(6-4/2)×6",
"(6-4)×6×2",
"(6×2-6)×4"
],
"2,4,6,7": [
"(6+2)×(7-4)",
"7×4+2-6",
"(6-2)×7-4",
"7×2+6+4",
"6/(2-7/4)"
],
"2,4,6,8": [
"8×6/(4-2)",
"8×6×2/4",
"8×4-6-2",
"(6+2)×4-8",
"6×2+8+4",
"(6-2)×4+8",
"(8/4+2)×6",
"(8+6)×2-4"
],
"2,4,6,9": [
"(9-6)×4×2",
"(4-2)×9+6",
"9×4/2+6",
"9×4-6×2",
"(9-6/2)×4",
"(4/6+2)×9",
"6/(9/4-2)"
],
"2,4,6,10": [
"(4+2)×(10-6)",
"(10-4-2)×6",
"4×2+10+6",
"(10+2-6)×4",
"(10-4)×(6-2)",
"(10+2)×(6-4)",
"(10+6-4)×2"
],
"2,4,6,11": [
"11×2+6-4",
"(6-4)×11+2",
"(11+4)×2-6",
"4/(2-11/6)"
],
"2,4,6,12": [
"12+6+4+2",
"(4+2)×6-12",
"(4×2-6)×12",
"(12-4×2)×6",
"(4-2)×6+12",
"6×4/2+12",
"(6+2)×12/4",
"(12-4)×6/2",
"(6×4-12)×2",
"12/(2-6/4)"
],
"2,4,6,13": [
"13×2+4-6",
"(6-4)×13-2",
"(13-4)×2+6",
"4/(13/6-2)"
],
"2,4,7,7": [
"(7+7)×2-4"
],
"2,4,7,8": [
"(7×2-8)×4",
"8×7/2-4",
"7×4-8/2"
],
"2,4,7,9": [
"4×2+9+7",
"(9+7-4)×2"
],
"2,4,7,10": [
"(10-7)×4×2",
"(4-2)×7+10",
"7×4/2+10",
"(10-2)×(7-4)"
],
"2,4,7,11": [
"11+7+4+2",
"(4+2)×(11-7)",
"(11+2-7)×4"
],
"2,4,7,12": [
"(7+2)×4-12",
"12/(4-7/2)"
],
"2,4,8,8": [
"4×2+8+8",
"(4-2)×8+8",
"8×4/2+8",
"(8-2)×(8-4)",
"(8+8-4)×2"
],
"2,4,8,9": [
"(9-4-2)×8"
],
"2,4,8,10": [
"10+8+4+2",
"10×4-8×2",
"(8×2-10)×4",
"(10-4)×8/2",
"(10-8/2)×4",
"(10+2)×8/4",
"10×2+8-4",
"8×4+2-10",
"(10-2)×4-8",
"(8/4+10)×2",
"(10×4+8)/2"
],
"2,4,8,11": [
"(11-8)×4×2",
"(11-4×2)×8",
"11×2+8/4",
"11×8/4+2"
],
"2,4,8,12": [
"(4+2)×(12-8)",
"(8-4-2)×12",
"8×2+12-4",
"(12+2-8)×4",
"(8-4)×12/2",
"(12+4)×2-8",
"(12-4)×2+8"
],
"2,4,8,13": [
"13×2-8/4",
"13×8/4-2"
],
"2,4,9,9": [
"9+9+4+2"
],
"2,4,9,10": [
"9×2+10-4",
"9×4-10-2"
],
"2,4,9,12": [
"(12-9)×4×2",
"(9×2-12)×4",
"12/(9/2-4)",
"(9×4+12)/2",
"(12/4+9)×2"
],
"2,4,9,13": [
"(4+2)×(13-9)",
"13+9+4-2",
"4/2+13+9",
"(13+2-9)×4"
],
"2,4,10,10": [
"(4/10+2)×10"
],
"2,4,10,11": [
"11×4-10×2",
"(11-10/2)×4",
"(11-4)×2+10"
],
"2,4,10,12": [
"(10-4×2)×12",
"12+10+4-2",
"4/2+12+10",
"(10-2)×12/4",
"(10-4)×2+12",
"12/(10/4-2)"
],
"2,4,10,13": [
"(13-10)×4×2",
"(13+4)×2-10"
],
"2,4,11,11": [
"11+11+4-2",
"4/2+11+11"
],
"2,4,11,12": [
"(11-2)×4-12"
],
"2,4,12,12": [
"12×12/(4+2)",
"12×4-12×2",
"(12/2-4)×12",
"(12-12/2)×4"
],
"2,4,13,13": [
"13+13+2-4",
"13+13-4/2"
],
"2,5,5,7": [
"7×2+5+5"
],
"2,5,5,8": [
"(5/5+2)×8"
],
"2,5,5,9": [
"5×2+9+5",
"(5-2)×5+9"
],
"2,5,5,10": [
"(5-2/10)×5"
],
"2,5,5,11": [
"(5+2)×5-11",
"(5/5+11)×2"
],
"2,5,5,12": [
"12+5+5+2",
"12×5×2/5",
"12×2+5-5"
],
"2,5,5,13": [
"(13-5)×(5-2)",
"(5×5-13)×2",
"(13-5/5)×2"
],
"2,5,6,6": [
"(5×2-6)×6",
"(5-2)×6+6"
],
"2,5,6,7": [
"(7+2-5)×6",
"6×2+7+5",
"(7-5)×6×2"
],
"2,5,6,8": [
"5×2+8+6",
"(6+2-5)×8",
"(6+2)×(8-5)",
"6×5+2-8",
"(8-2)×5-6"
],
"2,5,6,9": [
"6×5/2+9"
],
"2,5,6,10": [
"(5-2)×10-6",
"10×6×2/5",
"(10+5)×2-6",
"(10/5+2)×6"
],
"2,5,6,11": [
"11+6+5+2",
"(11-5-2)×6",
"(11-5)×(6-2)",
"(11+6-5)×2"
],
"2,5,6,12": [
"12×6/(5-2)",
"12×5/2-6",
"(5-6/2)×12",
"(6-5)×12×2",
"6×5-12/2"
],
"2,5,6,13": [
"(13-5)×6/2",
"(13+5-6)×2"
],
"2,5,7,7": [
"5×2+7+7"
],
"2,5,7,8": [
"(5×2-7)×8"
],
"2,5,7,9": [
"7×5-9-2"
],
"2,5,7,10": [
"10+7+5+2",
"(10+2)×(7-5)",
"(10+7-5)×2"
],
"2,5,7,11": [
"11×2+7-5",
"(7-5)×11+2",
"(11×5-7)/2"
],
"2,5,7,13": [
"13×2+5-7",
"7×5+2-13",
"(7×5+13)/2",
"(7-5)×13-2"
],
"2,5,8,8": [
"8×5-8×2",
"(8×5+8)/2"
],
"2,5,8,9": [
"9+8+5+2",
"9×8/(5-2)",
"(8-2)×(9-5)",
"(9+8-5)×2"
],
"2,5,8,10": [
"(10-5-2)×8",
"(10-2)×(8-5)"
],
"2,5,8,11": [
"(11-5)×8/2",
"(11+5)×2-8"
],
"2,5,8,12": [
"(5×2-8)×12",
"(8+2)×12/5"
],
"2,5,8,13": [
"(13-5×2)×8",
"13+8+5-2",
"8×2+13-5",
"(13+2)×8/5",
"(13-5)×2+8"
],
"2,5,9,10": [
"10×2+9-5"
],
"2,5,9,11": [
"(5-2)×11-9",
"9×2+11-5",
"(9-2)×5-11"
],
"2,5,9,12": [
"(9-5-2)×12",
"12+9+5-2",
"12/(5-9/2)",
"(9-5)×12/2"
],
"2,5,10,10": [
"(10+2)×10/5",
"(10/5+10)×2"
],
"2,5,10,11": [
"11+10+5-2",
"11×2+10/5",
"11×10/5+2"
],
"2,5,10,12": [
"(12+5)×2-10",
"(12-5)×2+10"
],
"2,5,10,13": [
"10×5-13×2",
"13×2-10/5",
"13×10/5-2"
],
"2,5,11,12": [
"12/(11/2-5)",
"(11-5)×2+12"
],
"2,5,12,12": [
"(12-5×2)×12",
"(5-2)×12-12",
"(12-2)×12/5",
"(12×5-12)/2"
],
"2,5,12,13": [
"12/2+13+5",
"(13+5)×2-12"
],
"2,6,6,6": [
"6×2+6+6",
"6×6-6×2",
"6×6/2+6"
],
"2,6,6,7": [
"(7-6/2)×6",
"(7-2)×6-6",
"(7×6+6)/2"
],
"2,6,6,8": [
"(8-6)×6×2",
"(6×2-8)×6",
"(8+2-6)×6",
"(6-6/2)×8",
"(6/6+2)×8"
],
"2,6,6,9": [
"(6+2)×(9-6)",
"(9+6)×2-6",
"(9×6-6)/2"
],
"2,6,6,10": [
"10+6+6+2",
"10×6/2-6",
"6×6-10-2"
],
"2,6,6,11": [
"(6/6+11)×2"
],
"2,6,6,12": [
"(12-6-2)×6",
"12×6×2/6",
"(12-6)×(6-2)",
"12×2+6-6",
"(6×6+12)/2",
"(12/6+2)×6"
],
"2,6,6,13": [
"(13-6/6)×2"
],
"2,6,7,8": [
"(7+2-6)×8",
"(8+7)×2-6"
],
"2,6,7,9": [
"9+7+6+2",
"(9-7)×6×2",
"(9+2-7)×6",
"7×6-9×2"
],
"2,6,7,10": [
"(6+2)×(10-7)",
"(7×2-10)×6"
],
"2,6,7,11": [
"(11+7-6)×2"
],
"2,6,7,12": [
"(7-6)×12×2"
],
"2,6,7,13": [
"13+7+6-2",
"(13-7)×(6-2)",
"(13-7-2)×6",
"(13+6-7)×2"
],
"2,6,8,8": [
"8+8+6+2",
"(6-2)×8-8",
"(8-8/2)×6"
],
"2,6,8,9": [
"(6×2-9)×8",
"9×8×2/6"
],
"2,6,8,10": [
"(10-8)×6×2",
"(10+2-8)×6",
"(8-2)×(10-6)",
"(10+2)×(8-6)",
"(10+8-6)×2",
"(10+6)×2-8",
"8/(2-10/6)"
],
"2,6,8,11": [
"(6+2)×(11-8)",
"(11-6-2)×8",
"11×2+8-6",
"(8-6)×11+2"
],
"2,6,8,12": [
"12+8+6-2",
"12×8/(6-2)",
"(8×2-12)×6",
"(8-2)×6-12",
"(12-6)×8/2",
"(6-8/2)×12",
"8×6-12×2"
],
"2,6,8,13": [
"6/2+13+8",
"13×2+6-8",
"(8-6)×13-2"
],
"2,6,9,9": [
"(9+9-6)×2",
"(6/9+2)×9"
],
"2,6,9,10": [
"(10-2)×(9-6)",
"(9-10/2)×6"
],
"2,6,9,11": [
"(11-9)×6×2",
"11+9+6-2",
"11×6/2-9",
"(11+2-9)×6"
],
"2,6,9,12": [
"(6+2)×(12-9)",
"(6-2)×9-12",
"6/2+12+9",
"9×2+12-6",
"12/(2-9/6)"
],
"2,6,10,10": [
"10+10+6-2",
"10×2+10-6"
],
"2,6,10,11": [
"6/2+11+10",
"(11+6)×2-10"
],
"2,6,10,12": [
"(10-6-2)×12",
"(12-10)×6×2",
"(6×2-10)×12",
"(10+2)×12/6",
"(12+2-10)×6",
"(10-6)×12/2",
"(10-12/2)×6",
"(10×6-12)/2",
"(12/6+10)×2"
],
"2,6,10,13": [
"(6+2)×(13-10)",
"10/2+13+6",
"(13-6)×2+10"
],
"2,6,11,12": [
"11×2+12/6",
"12/(6-11/2)",
"12×11/6+2"
],
"2,6,11,13": [
"(13-11)×6×2",
"(13+2-11)×6"
],
"2,6,12,12": [
"12×6/2-12",
"12/2+12+6",
"(12+6)×2-12",
"(12-6)×2+12"
],
"2,6,12,13": [
"13×2-12/6",
"12/(13/2-6)",
"13×12/6-2"
],
"2,7,7,8": [
"8+7+7+2",
"(7/7+2)×8"
],
"2,7,7,10": [
"(10/7+2)×7"
],
"2,7,7,11": [
"(7-2)×7-11",
"(7/7+11)×2"
],
"2,7,7,12": [
"12×7×2/7",
"12+7+7-2",
"12×2+7-7"
],
"2,7,7,13": [
"(13-7/7)×2"
],
"2,7,8,8": [
"(8+2-7)×8",
"(7-8/2)×8",
"(8×7-8)/2"
],
"2,7,8,9": [
"(9+7)×2-8"
],
"2,7,8,11": [
"(7×2-11)×8",
"11+8+7-2",
"(8-2)×(11-7)",
"(11+8-7)×2"
],
"2,7,8,12": [
"(12-7-2)×8",
"(8-7)×12×2"
],
"2,7,8,13": [
"(13-7)×8/2",
"8/2+13+7",
"(13+7-8)×2"
],
"2,7,9,10": [
"10+9+7-2",
"(10+2)×(9-7)",
"(10+9-7)×2"
],
"2,7,9,11": [
"11×2+9-7",
"(9-7)×11+2"
],
"2,7,9,13": [
"9×2+13-7",
"13×2+7-9",
"(9-7)×13-2"
],
"2,7,10,10": [
"(10-2)×(10-7)",
"(10+7)×2-10"
],
"2,7,10,11": [
"10×7/2-11",
"10×2+11-7"
],
"2,7,10,12": [
"12×10/(7-2)",
"10/2+12+7",
"(7-10/2)×12"
],
"2,7,11,12": [
"(11-7-2)×12",
"(11-7)×12/2",
"12/2+11+7",
"(11+7)×2-12"
],
"2,7,12,12": [
"(7×2-12)×12",
"(12+2)×12/7"
],
"2,7,12,13": [
"12/(7-13/2)",
"(13-7)×2+12"
],
"2,8,8,8": [
"8×8/2-8",
"(8+8)×2-8",
"(8/8+2)×8"
],
"2,8,8,9": [
"(9+2-8)×8"
],
"2,8,8,10": [
"10+8+8-2",
"(8-10/2)×8"
],
"2,8,8,11": [
"(8/8+11)×2"
],
"2,8,8,12": [
"12×8×2/8",
"(8-2)×(12-8)",
"8/2+12+8",
"12×2+8-8"
],
"2,8,8,13": [
"(13-8-2)×8",
"(8×2-13)×8",
"(13-8/8)×2"
],
"2,8,9,9": [
"9+9+8-2",
"(9/9+2)×8"
],
"2,8,9,10": [
"(10+2-9)×8",
"(9+8)×2-10"
],
"2,8,9,11": [
"8/2+11+9",
"(11+9-8)×2"
],
"2,8,9,12": [
"9×8/2-12",
"(9-8)×12×2",
"(9-12/2)×8",
"(8/12+2)×9"
],
"2,8,9,13": [
"(8-2)×(13-9)",
"(13+8-9)×2",
"9/(2-13/8)"
],
"2,8,10,10": [
"8/2+10+10",
"(10+2)×(10-8)",
"(10+10-8)×2",
"(10/10+2)×8"
],
"2,8,10,11": [
"(11+2-10)×8",
"(10-2)×(11-8)",
"10/2+11+8",
"11×2+10-8",
"(10-8)×11+2"
],
"2,8,10,12": [
"10×2+12-8",
"12/2+10+8",
"(10+8)×2-12"
],
"2,8,10,13": [
"13×2+8-10",
"(10-8)×13-2"
],
"2,8,11,11": [
"(11/11+2)×8"
],
"2,8,11,12": [
"(12+2-11)×8"
],
"2,8,12,12": [
"(12-8-2)×12",
"12×12/(8-2)",
"(12-8)×12/2",
"(8-12/2)×12",
"12/(2-12/8)",
"(12/12+2)×8"
],
"2,8,12,13": [
"(13+2-12)×8"
],
"2,8,13,13": [
"(13/13+2)×8"
],
"2,9,9,11": [
"(9/9+11)×2"
],
"2,9,9,12": [
"12×9×2/9",
"12×2+9-9",
"12/2+9+9",
"(9+9)×2-12"
],
"2,9,9,13": [
"(13-9/9)×2"
],
"2,9,10,10": [
"10/2+10+9"
],
"2,9,10,11": [
"(10+2)×(11-9)",
"(11+10-9)×2"
],
"2,9,10,12": [
"(10-2)×(12-9)",
"(10-9)×12×2"
],
"2,9,10,13": [
"10×2+13-9",
"(13+9-10)×2"
],
"2,9,11,11": [
"11×2+11-9",
"(11-9)×11+2"
],
"2,9,11,13": [
"13×2+9-11",
"(11-9)×13-2"
],
"2,9,12,13": [
"(13-9-2)×12",
"(13-9)×12/2"
],
"2,9,13,13": [
"(13+9)/2+13"
],
"2,10,10,11": [
"(10/10+11)×2"
],
"2,10,10,12": [
"(10+2)×(12-10)",
"12×10×2/10",
"12×2+10-10"
],
"2,10,10,13": [
"(10-2)×(13-10)",
"(13-10/10)×2"
],
"2,10,11,11": [
"(11+11-10)×2"
],
"2,10,11,12": [
"11×2+12-10",
"(11-10)×12×2",
"(12-10)×11+2"
],
"2,10,11,13": [
"(10+2)×(13-11)",
"(13+10-11)×2"
],
"2,10,12,13": [
"13×2+10-12",
"(12+10)/2+13",
"(12-10)×13-2"
],
"2,11,11,11": [
"(11/11+11)×2"
],
"2,11,11,12": [
"12×11×2/11",
"12×2+11-11"
],
"2,11,11,13": [
"11×2+13-11",
"(11+11)/2+13",
"(13-11/11)×2",
"(13-11)×11+2"
],
"2,11,12,12": [
"(12-11)×12×2",
"(12/12+11)×2"
],
"2,11,12,13": [
"(13+11-12)×2",
"(13+11)/2+12"
],
"2,11,13,13": [
"13×2+11-13",
"(13-11)×13-2",
"(13+13)/2+11",
"(13/13+11)×2"
],
"2,12,12,12": [
"12×2+12-12",
"12×12×2/12",
"(12+12)/2+12"
],
"2,12,12,13": [
"(13-12)×12×2",
"(13-12/12)×2"
],
"2,12,13,13": [
"12×2+13-13",
"13×12×2/13"
],
"2,13,13,13": [
"(13-13/13)×2"
],
"3,3,3,3": [
"3×3×3-3"
],
"3,3,3,4": [
"(3×3-3)×4",
"(4+3)×3+3"
],
"3,3,3,5": [
"5×3+3×3"
],
"3,3,3,6": [
"6×3+3+3",
"(3+3)×3+6",
"(3/3+3)×6",
"(6+3)×3-3"
],
"3,3,3,7": [
"(3+3)×(7-3)",
"(3/3+7)×3"
],
"3,3,3,8": [
"8×3×3/3",
"8×3+3-3"
],
"3,3,3,9": [
"(9-3/3)×3"
],
"3,3,3,10": [
"10×3-3-3",
"(10-3)×3+3"
],
"3,3,3,11": [
"11×3-3×3"
],
"3,3,3,12": [
"(3+3)×12/3",
"3×3+12+3",
"(3-3/3)×12",
"(12-3)×3-3"
],
"3,3,4,4": [
"4×3+4×3",
"(4×3-4)×3"
],
"3,3,4,5": [
"(3/3+5)×4",
"(5-3)×4×3",
"(5+4)×3-3"
],
"3,3,4,6": [
"6×4+3-3",
"6×4×3/3"
],
"3,3,4,7": [
"(7-3/3)×4",
"(7+4-3)×3"
],
"3,3,4,8": [
"(3+3)×(8-4)",
"(4-3/3)×8",
"(4-3)×8×3"
],
"3,3,4,9": [
"4×3+9+3",
"(9+3-4)×3",
"(9/3+3)×4"
],
"3,3,4,11": [
"3×3+11+4",
"(11-4)×3+3"
],
"3,3,4,12": [
"(3+3-4)×12",
"(12-3-3)×4",
"4×3×3-12",
"12×3-4×3",
"(12/3+4)×3"
],
"3,3,4,13": [
"(13-4)×3-3"
],
"3,3,5,5": [
"5×5-3/3"
],
"3,3,5,6": [
"6×5-3-3",
"(3+3)×5-6",
"(3×3-5)×6",
"(5-3/3)×6",
"(5+3)×(6-3)",
"5×3+6+3",
"(6+5-3)×3"
],
"3,3,5,7": [
"(5×3-7)×3"
],
"3,3,5,9": [
"(3+3)×(9-5)",
"(5+3)×9/3",
"(9+3)×(5-3)",
"(9/3+5)×3"
],
"3,3,5,10": [
"3×3+10+5",
"(10+3-5)×3",
"(3-3/5)×10"
],
"3,3,5,12": [
"5×3+12-3",
"(12-5)×3+3"
],
"3,3,5,13": [
"13+5+3+3",
"13×3-5×3"
],
"3,3,6,6": [
"(6/3+6)×3"
],
"3,3,6,7": [
"7×3+6-3",
"(6-3)×7+3",
"(7+3)×3-6"
],
"3,3,6,8": [
"(3×3-6)×8",
"(6+3)×8/3"
],
"3,3,6,9": [
"3×3+9+6",
"6×3+9-3",
"9×3+3-6",
"(6-3)×9-3",
"(9+3)×6/3",
"(9-3)×3+6"
],
"3,3,6,10": [
"(3+3)×(10-6)",
"(10-3-3)×6",
"(6×3-10)×3",
"(10-6/3)×3"
],
"3,3,6,11": [
"11×3-6-3",
"(11+3-6)×3",
"(11-3)×(6-3)"
],
"3,3,6,12": [
"12+6+3+3",
"(3+3)×6-12"
],
"3,3,6,13": [
"(13-3×3)×6",
"(13-3)×3-6",
"(13-6)×3+3"
],
"3,3,7,7": [
"(3/7+3)×7"
],
"3,3,7,8": [
"3×3+8+7"
],
"3,3,7,9": [
"7×3+9/3",
"(9-3)×(7-3)",
"9×7/3+3"
],
"3,3,7,11": [
"11+7+3+3",
"(3+3)×(11-7)"
],
"3,3,7,12": [
"(3×3-7)×12",
"(12+3-7)×3",
"(7-3)×3+12"
],
"3,3,7,13": [
"(7×3-13)×3"
],
"3,3,8,8": [
"8/(3-8/3)"
],
"3,3,8,9": [
"(9-3-3)×8",
"(8+3)×3-9",
"(8-3)×3+9"
],
"3,3,8,10": [
"10+8+3+3",
"8/(10/3-3)"
],
"3,3,8,12": [
"(3+3)×(12-8)",
"(8-3-3)×12",
"(12-3×3)×8",
"(12-3)×8/3"
],
"3,3,8,13": [
"(13+3-8)×3"
],
"3,3,9,9": [
"9+9+3+3",
"9×3-9/3",
"(3-3/9)×9",
"9×9/3-3"
],
"3,3,9,10": [
"10×3+3-9"
],
"3,3,9,11": [
"(11-3)×9/3",
"(11-9/3)×3"
],
"3,3,9,12": [
"12×3-9-3",
"(9+3)×3-12",
"(9-3)×12/3"
],
"3,3,9,13": [
"(3+3)×(13-9)"
],
"3,3,10,13": [
"3/3+13+10"
],
"3,3,11,12": [
"(11-3×3)×12",
"3/3+12+11",
"11×3+3-12"
],
"3,3,11,13": [
"13+11+3-3",
"(13+11)×3/3"
],
"3,3,12,12": [
"12×12/(3+3)",
"12+12+3-3",
"(12+12)×3/3",
"(12-12/3)×3"
],
"3,3,12,13": [
"13+12-3/3",
"13×3-12-3"
],
"3,4,4,4": [
"(4+3)×4-4"
],
"3,4,4,5": [
"(5+4-3)×4",
"4×4+5+3"
],
"3,4,4,6": [
"(6-4)×4×3",
"(4×3-6)×4",
"(4-3)×6×4",
"(4+4)×(6-3)",
"(6/3+4)×4",
"(4/4+3)×6"
],
"3,4,4,7": [
"(7+3-4)×4",
"(4/4+7)×3"
],
"3,4,4,8": [
"4×3+8+4",
"8×4×3/4",
"8×3+4-4",
"(8-3)×4+4",
"(4×4-8)×3"
],
"3,4,4,9": [
"9×4-4×3",
"(4-4/3)×9",
"(4+4)×9/3",
"(9-4/4)×3"
],
"3,4,4,10": [
"(10-3)×4-4"
],
"3,4,4,11": [
"4×4+11-3"
],
"3,4,4,12": [
"(3-4/4)×12",
"(12/4+3)×4"
],
"3,4,4,13": [
"13+4+4+3",
"(13-4-3)×4"
],
"3,4,5,5": [
"5×5+3-4",
"5×3+5+4"
],
"3,4,5,6": [
"(5+3-4)×6"
],
"3,4,5,7": [
"4×3+7+5",
"(7-5)×4×3",
"(5+3)×(7-4)",
"5×4+7-3",
"(7-3)×5+4",
"(7+5-4)×3"
],
"3,4,5,8": [
"8×4-5-3",
"(5+3)×4-8",
"(8+3-5)×4",
"(8+4)×(5-3)",
"(5-4)×8×3",
"(5+4)×8/3"
],
"3,4,5,9": [
"(5×3-9)×4",
"(9+4-5)×3"
],
"3,4,5,10": [
"10×4×3/5",
"(5-3)×10+4"
],
"3,4,5,11": [
"(4+3)×5-11",
"11×3-5-4"
],
"3,4,5,12": [
"12+5+4+3",
"(4+3-5)×12",
"(5+3)×12/4",
"12×4/(5-3)",
"12×5/3+4",
"5×4+12/3",
"(5×4-12)×3",
"(12/4+5)×3"
],
"3,4,5,13": [
"(13+5)×4/3",
"5×3+13-4"
],
"3,4,6,6": [
"4×3+6+6",
"6×6-4×3",
"(6+4)×3-6",
"(6+6-4)×3"
],
"3,4,6,8": [
"(8-6)×4×3",
"(4×3-8)×6",
"(8+4)×6/3",
"(8-6/3)×4",
"(8/4+6)×3"
],
"3,4,6,9": [
"(9+3-6)×4",
"(9+3)×(6-4)"
],
"3,4,6,10": [
"6×3+10-4",
"10×6/3+4",
"(10+4-6)×3",
"(10-4)×3+6"
],
"3,4,6,11": [
"11+6+4+3",
"(11-4-3)×6",
"6/(3-11/4)"
],
"3,4,6,12": [
"12×4×3/6",
"(12+6)×4/3",
"(6+3)×4-12",
"(6×3-12)×4",
"(12-4)×(6-3)",
"(6-3)×4+12",
"(4-6/3)×12"
],
"3,4,6,13": [
"(13+3)×6/4",
"6/(13/4-3)"
],
"3,4,7,7": [
"7×3+7-4",
"7×4+3-7",
"(7-3)×7-4",
"(7-4)×7+3"
],
"3,4,7,8": [
"(7-3)×4+8"
],
"3,4,7,9": [
"(9-7)×4×3",
"9×3+4-7",
"(7+4)×3-9",
"(7-4)×9-3"
],
"3,4,7,10": [
"10+7+4+3",
"(10+3-7)×4",
"(10-4)×(7-3)"
],
"3,4,7,11": [
"(11+7)×4/3",
"(11-3)×(7-4)",
"(11+4-7)×3"
],
"3,4,7,12": [
"7×3+12/4",
"12×7/3-4",
"7×4-12/3",
"12×7/4+3"
],
"3,4,8,9": [
"9+8+4+3",
"(4×3-9)×8",
"(9+3)×8/4",
"(9-3)×(8-4)"
],
"3,4,8,10": [
"(10-4-3)×8",
"(10-8)×4×3",
"(10+8)×4/3",
"(10-8/4)×3"
],
"3,4,8,11": [
"(11+3-8)×4",
"8×4+3-11",
"(11-3)×4-8",
"8/(4-11/3)"
],
"3,4,8,12": [
"12×4/3+8",
"12×4-8×3",
"12×3-8-4",
"(8+4)×3-12",
"(12+4-8)×3",
"(8-4)×3+12"
],
"3,4,8,13": [
"(13-4)×8/3",
"8/(13/3-4)"
],
"3,4,9,9": [
"(9+9)×4/3",
"9×4-9-3",
"(9-9/3)×4",
"(9-4)×3+9"
],
"3,4,9,11": [
"(11-9)×4×3",
"(11×9-3)/4"
],
"3,4,9,12": [
"(9-4-3)×12",
"9×4/3+12",
"9×3-12/4",
"(12+3-9)×4",
"(12-4)×9/3",
"12×9/4-3",
"(3-4/12)×9"
],
"3,4,9,13": [
"(13+4-9)×3"
],
"3,4,10,10": [
"10×3+4-10"
],
"3,4,10,12": [
"(12-10)×4×3",
"(4×3-10)×12",
"(10-4)×12/3",
"(10-12/3)×4",
"12/(3-10/4)"
],
"3,4,10,13": [
"13+10+4-3",
"(13+3-10)×4",
"10×4-13-3"
],
"3,4,11,12": [
"12+11+4-3",
"(11-3)×12/4",
"(11-12/4)×3"
],
"3,4,11,13": [
"(13-11)×4×3",
"(13+11)×(4-3)",
"11×3+4-13",
"13×3-11-4"
],
"3,4,12,12": [
"(12+12)×(4-3)",
"(12-3)×4-12"
],
"3,4,12,13": [
"13+12+3-4"
],
"3,5,5,6": [
"(5+5)×3-6",
"(5/5+3)×6"
],
"3,5,5,7": [
"(7+5)×(5-3)",
"(5/5+7)×3"
],
"3,5,5,8": [
"(5+3)×(8-5)",
"8×5×3/5",
"8×3+5-5"
],
"3,5,5,9": [
"(9-5/5)×3",
"(9/5+3)×5"
],
"3,5,5,11": [
"11+5+5+3"
],
"3,5,5,12": [
"(3-5/5)×12"
],
"3,5,6,6": [
"(6+3-5)×6",
"(6+6)×(5-3)"
],
"3,5,6,7": [
"(7+5)×6/3",
"(7+6-5)×3"
],
"3,5,6,8": [
"8×6/(5-3)",
"(5-6/3)×8",
"(6-5)×8×3"
],
"3,5,6,9": [
"(5+3)×(9-6)",
"(5-3)×9+6",
"(6-3)×5+9",
"6×5+3-9",
"(9-3)×5-6",
"(6+5)×3-9",
"(9+5-6)×3"
],
"3,5,6,10": [
"10+6+5+3",
"(10/5+6)×3"
],
"3,5,6,11": [
"(5×3-11)×6",
"6×3+11-5",
"(11-5)×3+6"
],
"3,5,6,12": [
"(5+3-6)×12",
"(12-5-3)×6",
"(5-3)×6+12"
],
"3,5,6,13": [
"(13-5)×(6-3)"
],
"3,5,7,8": [
"7×3+8-5",
"7×5-8-3",
"(8-5)×7+3"
],
"3,5,7,9": [
"9+7+5+3",
"9×5-7×3",
"(5-7/3)×9",
"(9+3)×(7-5)"
],
"3,5,7,10": [
"(5+3)×(10-7)",
"(5-3)×7+10",
"(10+5-7)×3"
],
"3,5,7,11": [
"(11-5)×(7-3)",
"(11×7-5)/3"
],
"3,5,7,12": [
"(7+3)×12/5",
"12×3-7-5",
"(7+5)×3-12"
],
"3,5,7,13": [
"(13×5+7)/3"
],
"3,5,8,8": [
"8+8+5+3",
"(5-3)×8+8"
],
"3,5,8,9": [
"9×3+5-8",
"(8-5)×9-3"
],
"3,5,8,11": [
"(5+3)×(11-8)",
"(11-5-3)×8",
"(11-3)×(8-5)",
"(11+5-8)×3"
],
"3,5,8,12": [
"(5×3-12)×8",
"(12+3)×8/5"
],
"3,5,8,13": [
"8×5-13-3"
],
"3,5,9,9": [
"9×5/3+9",
"(9-3)×(9-5)"
],
"3,5,9,10": [
"(9+3)×10/5",
"(10-5)×3+9"
],
"3,5,9,12": [
"(5+3)×(12-9)",
"(5-9/3)×12",
"(12+5-9)×3",
"(9-5)×3+12"
],
"3,5,9,13": [
"13+9+5-3",
"(13-5)×9/3",
"(13×9+3)/5"
],
"3,5,10,10": [
"(10-10/5)×3"
],
"3,5,10,11": [
"10×3+5-11",
"(10-3)×5-11"
],
"3,5,10,12": [
"(10-5-3)×12",
"12+10+5-3"
],
"3,5,10,13": [
"(5+3)×(13-10)",
"13×3-10-5",
"(13+5-10)×3"
],
"3,5,11,11": [
"11+11+5-3"
],
"3,5,11,12": [
"(11-5)×12/3"
],
"3,5,12,12": [
"12×5-12×3",
"(12×5+12)/3"
],
"3,5,12,13": [
"(5×3-13)×12",
"(13-3)×12/5"
],
"3,5,13,13": [
"13+13+3-5"
],
"3,6,6,6": [
"(6-3)×6+6",
"(6+6)×6/3",
"(6-6/3)×6",
"(6/6+3)×6"
],
"3,6,6,7": [
"7×6-6×3",
"(7+3-6)×6",
"(6/6+7)×3"
],
"3,6,6,8": [
"8×6×3/6",
"8×3+6-6",
"(8-3)×6-6"
],
"3,6,6,9": [
"9+6+6+3",
"9×6/3+6",
"6×6-9-3",
"(9-6/6)×3"
],
"3,6,6,10": [
"(6-3)×10-6"
],
"3,6,6,11": [
"(11×6+6)/3"
],
"3,6,6,12": [
"6×3+12-6",
"12×6/(6-3)",
"6×6/3+12",
"12×3-6-6",
"(6+6)×3-12",
"(3-6/6)×12",
"(12-6)×3+6",
"(12/6+6)×3"
],
"3,6,6,13": [
"(13-6-3)×6",
"(13×6-6)/3"
],
"3,6,7,7": [
"(7+7-6)×3",
"(7/7+3)×6"
],
"3,6,7,8": [
"8+7+6+3",
"(8+3-7)×6",
"(7-6)×8×3"
],
"3,6,7,9": [
"7×3+9-6",
"(7-9/3)×6",
"(9+6-7)×3",
"(9-6)×7+3"
],
"3,6,7,10": [
"7×6/3+10"
],
"3,6,7,12": [
"(6+3-7)×12",
"(12-6)×(7-3)"
],
"3,6,7,13": [
"6×3+13-7",
"(13-7)×3+6"
],
"3,6,8,8": [
"8×6/3+8",
"8×6-8×3",
"(8/8+3)×6"
],
"3,6,8,9": [
"9×8/(6-3)",
"(9+3-8)×6",
"(9+3)×(8-6)",
"(6-9/3)×8"
],
"3,6,8,10": [
"(10+6-8)×3"
],
"3,6,8,12": [
"(12-6-3)×8",
"(8-12/3)×6"
],
"3,6,8,13": [
"13+8+6-3"
],
"3,6,9,9": [
"9×3+6-9",
"(9-6)×9-3",
"(9/9+3)×6"
],
"3,6,9,10": [
"(10+3-9)×6",
"(9-3)×(10-6)",
"10×9/3-6",
"9×6-10×3",
"(6-10/3)×9"
],
"3,6,9,11": [
"(6-3)×11-9",
"(11-3)×(9-6)",
"(11+6-9)×3",
"(11-6)×3+9"
],
"3,6,9,12": [
"12×6×3/9",
"12+9+6-3",
"(9+3)×12/6",
"(9-3)×6-12"
],
"3,6,9,13": [
"6/3+13+9",
"(13+3)×9/6",
"13×3-9-6"
],
"3,6,10,10": [
"(3-6/10)×10",
"(10/10+3)×6"
],
"3,6,10,11": [
"11+10+6-3",
"(11+3-10)×6"
],
"3,6,10,12": [
"6/3+12+10",
"10×3+6-12",
"10×6-12×3",
"(10×6+12)/3",
"(12+6-10)×3",
"(10-6)×3+12",
"(10-12/6)×3"
],
"3,6,11,11": [
"6/3+11+11",
"(11/11+3)×6"
],
"3,6,11,12": [
"(11-6-3)×12",
"(12+3-11)×6"
],
"3,6,11,13": [
"(13+6-11)×3"
],
"3,6,12,12": [
"(6-3)×12-12",
"(12-6)×12/3",
"(6-12/3)×12",
"(12/12+3)×6"
],
"3,6,12,13": [
"(13+3-12)×6"
],
"3,6,13,13": [
"13+13-6/3",
"(13/13+3)×6"
],
"3,7,7,7": [
"7+7+7+3",
"(7/7+7)×3"
],
"3,7,7,8": [
"8×7×3/7",
"8×3+7-7"
],
"3,7,7,9": [
"(9-7/7)×3"
],
"3,7,7,10": [
"7×3+10-7",
"(10-7)×7+3"
],
"3,7,7,12": [
"(3-7/7)×12"
],
"3,7,7,13": [
"13+7+7-3",
"(13-7)×(7-3)"
],
"3,7,8,8": [
"(7-3)×8-8",
"(8-7)×8×3",
"(8/8+7)×3"
],
"3,7,8,9": [
"(9+7-8)×3"
],
"3,7,8,11": [
"7×3+11-8",
"(8-3)×7-11",
"(11-8)×7+3"
],
"3,7,8,12": [
"(7+3-8)×12",
"12+8+7-3",
"12×8/(7-3)",
"(7-12/3)×8"
],
"3,7,8,13": [
"(13-7-3)×8",
"13×3-8-7"
],
"3,7,9,9": [
"(9+3)×(9-7)",
"(9×7+9)/3",
"(9/9+7)×3"
],
"3,7,9,10": [
"9×3+7-10",
"(10+7-9)×3",
"(10-7)×9-3"
],
"3,7,9,11": [
"11+9+7-3",
"(9-3)×(11-7)"
],
"3,7,9,12": [
"7×3+12-9",
"(7-3)×9-12",
"(12-7)×3+9",
"(12-9)×7+3"
],
"3,7,9,13": [
"9×7-13×3",
"(7-13/3)×9"
],
"3,7,10,10": [
"10+10+7-3",
"(10/10+7)×3"
],
"3,7,10,11": [
"(11-3)×(10-7)",
"(11+7-10)×3"
],
"3,7,10,13": [
"7×3+13-10",
"10×3+7-13",
"(13-10)×7+3"
],
"3,7,11,11": [
"(11/11+7)×3"
],
"3,7,11,12": [
"(11+3)×12/7",
"(12+7-11)×3",
"(11-7)×3+12"
],
"3,7,12,12": [
"(12-7-3)×12",
"(12×7-12)/3",
"(12/12+7)×3"
],
"3,7,12,13": [
"(13-7)×12/3",
"12/3+13+7",
"(13+7-12)×3"
],
"3,7,13,13": [
"(13/13+7)×3"
],
"3,8,8,8": [
"8×3+8-8",
"8×8×3/8",
"(8×8+8)/3"
],
"3,8,8,9": [
"(9-8)×8×3",
"(9-8/8)×3"
],
"3,8,8,10": [
"(10×8-8)/3"
],
"3,8,8,11": [
"11+8+8-3"
],
"3,8,8,12": [
"12×8/3-8",
"(3-8/8)×12"
],
"3,8,9,9": [
"8×3+9-9",
"9×8×3/9"
],
"3,8,9,10": [
"(10-9)×8×3",
"10+9+8-3",
"(9+3)×(10-8)"
],
"3,8,9,11": [
"9×3+8-11",
"(11-8)×9-3"
],
"3,8,9,12": [
"(8+3-9)×12",
"(9-3)×(12-8)"
],
"3,8,9,13": [
"9/3+13+8",
"(13-8)×3+9"
],
"3,8,10,10": [
"8×3+10-10",
"10×8×3/10"
],
"3,8,10,11": [
"(11-10)×8×3"
],
"3,8,10,12": [
"12×10/(8-3)"
],
"3,8,11,11": [
"8×3+11-11",
"11×8×3/11",
"(11-3)×(11-8)"
],
"3,8,11,12": [
"(12-11)×8×3"
],
"3,8,12,12": [
"8×3+12-12",
"12×8×3/12",
"12/3+12+8",
"(12-8)×3+12"
],
"3,8,12,13": [
"(13-8-3)×12",
"(13-12)×8×3",
"(13+3)×12/8"
],
"3,8,13,13": [
"8×3+13-13",
"13×8×3/13"
],
"3,9,9,9": [
"9+9+9-3",
"(9×9-9)/3",
"(9-9/9)×3"
],
"3,9,9,10": [
"(9+9-10)×3"
],
"3,9,9,11": [
"(9+3)×(11-9)",
"11×9/3-9"
],
"3,9,9,12": [
"9×3+9-12",
"9/3+12+9",
"(3-9/9)×12",
"(12-9)×9-3"
],
"3,9,9,13": [
"(9-3)×(13-9)"
],
"3,9,10,10": [
"(9-10/10)×3"
],
"3,9,10,11": [
"9/3+11+10",
"(10+9-11)×3"
],
"3,9,10,12": [
"(9+3)×(12-10)",
"(9+3-10)×12"
],
"3,9,10,13": [
"9×3+10-13",
"(13-10)×9-3"
],
"3,9,11,11": [
"(3-9/11)×11",
"(9-11/11)×3"
],
"3,9,11,12": [
"(11-3)×(12-9)",
"12/3+11+9",
"(11+9-12)×3"
],
"3,9,11,13": [
"(9+3)×(13-11)"
],
"3,9,12,12": [
"12×12/(9-3)",
"12×9/3-12",
"(9-12/12)×3"
],
"3,9,12,13": [
"(12+9-13)×3",
"(13-9)×3+12"
],
"3,9,13,13": [
"(9-13/13)×3"
],
"3,10,10,12": [
"12/3+10+10",
"(10+10-12)×3",
"(3-10/10)×12"
],
"3,10,11,12": [
"(10+3-11)×12"
],
"3,10,11,13": [
"(11-3)×(13-10)",
"(11+10-13)×3"
],
"3,11,11,12": [
"(3-11/11)×12"
],
"3,11,12,12": [
"(11+3-12)×12"
],
"3,12,12,12": [
"(3-12/12)×12"
],
"3,12,12,13": [
"(12+3-13)×12"
],
"3,12,13,13": [
"(3-13/13)×12"
],
"4,4,4,4": [
"4×4+4+4"
],
"4,4,4,5": [
"(4/4+5)×4"
],
"4,4,4,6": [
"6×4×4/4",
"6×4+4-4"
],
"4,4,4,7": [
"(4+4)×(7-4)",
"(7-4/4)×4"
],
"4,4,4,8": [
"8×4-4-4",
"(4+4)×4-8",
"(4-4/4)×8",
"(8/4+4)×4"
],
"4,4,4,9": [
"(9-4)×4+4"
],
"4,4,4,10": [
"10×4-4×4",
"(4×4-10)×4"
],
"4,4,4,11": [
"(11-4)×4-4"
],
"4,4,4,12": [
"12+4+4+4",
"(4+4)×12/4",
"4×4+12-4"
],
"4,4,5,5": [
"5×5-4/4",
"(5+5-4)×4",
"(4/5+4)×5"
],
"4,4,5,6": [
"(5-4/4)×6",
"(5-4)×6×4"
],
"4,4,5,7": [
"(7+4-5)×4"
],
"4,4,5,8": [
"(4+4)×(8-5)",
"(4+4-5)×8",
"8×5-4×4",
"5×4+8-4",
"(8-4)×5+4"
],
"4,4,5,10": [
"(10-5)×4+4",
"(10/5+4)×4"
],
"4,4,5,11": [
"11+5+4+4",
"11×4-5×4"
],
"4,4,5,12": [
"(5+4)×4-12",
"(12-5)×4-4"
],
"4,4,5,13": [
"4×4+13-5"
],
"4,4,6,8": [
"(8+4-6)×4",
"(8+4)×(6-4)"
],
"4,4,6,9": [
"(4+4)×(9-6)",
"9×4×4/6"
],
"4,4,6,10": [
"10+6+4+4",
"(6-4)×10+4"
],
"4,4,6,11": [
"(11-6)×4+4"
],
"4,4,6,12": [
"(4+4-6)×12",
"(12-4-4)×6",
"(4×4-12)×6",
"12×4-6×4",
"12×4/(6-4)",
"(12+4)×6/4",
"(12/6+4)×4"
],
"4,4,6,13": [
"(13-6)×4-4"
],
"4,4,7,7": [
"(4-4/7)×7"
],
"4,4,7,8": [
"7×4+4-8",
"(8-4)×7-4"
],
"4,4,7,9": [
"9+7+4+4",
"(9+4-7)×4"
],
"4,4,7,10": [
"(4+4)×(10-7)"
],
"4,4,7,12": [
"(12-4)×(7-4)",
"(7-4)×4+12",
"(12-7)×4+4"
],
"4,4,7,13": [
"13×4-7×4"
],
"4,4,8,8": [
"8+8+4+4",
"(8+4)×8/4",
"(8-4)×4+8",
"(8-8/4)×4"
],
"4,4,8,9": [
"9×4-8-4"
],
"4,4,8,10": [
"(10+4-8)×4",
"(10-4)×(8-4)",
"10×8/4+4"
],
"4,4,8,11": [
"(4+4)×(11-8)",
"(11-4-4)×8"
],
"4,4,8,12": [
"12×4×4/8",
"8×4+4-12",
"(4-8/4)×12",
"(12-4)×4-8"
],
"4,4,8,13": [
"(4×4-13)×8",
"(13-8)×4+4"
],
"4,4,9,11": [
"(11+4-9)×4"
],
"4,4,9,12": [
"(4+4)×(12-9)",
"(9-12/4)×4"
],
"4,4,10,10": [
"(10×10-4)/4"
],
"4,4,10,12": [
"(10-4-4)×12",
"10×4-12-4",
"(12+4-10)×4"
],
"4,4,10,13": [
"(4+4)×(13-10)",
"4/4+13+10"
],
"4,4,11,12": [
"4/4+12+11"
],
"4,4,11,13": [
"13+11+4-4",
"(13+11)×4/4",
"(13+4-11)×4"
],
"4,4,12,12": [
"12+12+4-4",
"(12+12)×4/4",
"(12-4)×12/4"
],
"4,4,12,13": [
"13+12-4/4",
"(13-4)×4-12"
],
"4,5,5,5": [
"5×5+4-5",
"(5/5+5)×4"
],
"4,5,5,6": [
"6×5×4/5",
"6×4+5-5"
],
"4,5,5,7": [
"(7-5/5)×4"
],
"4,5,5,8": [
"(4-5/5)×8"
],
"4,5,5,9": [
"5×4+9-5",
"(9-5)×5+4"
],
"4,5,5,10": [
"10+5+5+4"
],
"4,5,6,6": [
"(6-5)×6×4",
"(6/6+5)×4"
],
"4,5,6,7": [
"(7+5)×(6-4)",
"(7+5-6)×4"
],
"4,5,6,8": [
"(5+4-6)×8"
],
"4,5,6,9": [
"9+6+5+4"
],
"4,5,6,10": [
"5×4+10-6",
"6×5+4-10",
"(10-4)×5-6",
"(10-6)×5+4"
],
"4,5,6,11": [
"(11+5)×6/4"
],
"4,5,6,12": [
"(6+4)×12/5"
],
"4,5,6,13": [
"(13-5-4)×6"
],
"4,5,7,7": [
"7×5-7-4",
"(7/7+5)×4"
],
"4,5,7,8": [
"8+7+5+4",
"(8+4)×(7-5)",
"(7+5)×8/4",
"(8+5-7)×4"
],
"4,5,7,9": [
"7×4+5-9",
"(7-4)×5+9",
"9×4-7-5",
"(9-5)×7-4"
],
"4,5,7,10": [
"(7-5)×10+4"
],
"4,5,7,11": [
"5×4+11-7",
"(11-7)×5+4"
],
"4,5,7,12": [
"(5+4-7)×12",
"12×4/(7-5)"
],
"4,5,7,13": [
"(13-5)×(7-4)",
"(13×7+5)/4"
],
"4,5,8,8": [
"(5-8/4)×8",
"(8/8+5)×4"
],
"4,5,8,9": [
"(9+5-8)×4",
"(9-5)×4+8"
],
"4,5,8,10": [
"(8+4)×10/5",
"(4-8/5)×10",
"(8-10/5)×4",
"(8/10+4)×5"
],
"4,5,8,11": [
"(11-5)×(8-4)",
"(11+4)×8/5"
],
"4,5,8,12": [
"(12-5-4)×8",
"5×4+12-8",
"8×5-12-4",
"(12-4)×(8-5)",
"(8-5)×4+12",
"(12-8)×5+4"
],
"4,5,8,13": [
"8×4+5-13",
"(13-5)×4-8"
],
"4,5,9,9": [
"(9/9+5)×4"
],
"4,5,9,10": [
"(10-4)×(9-5)",
"(10+5-9)×4"
],
"4,5,9,12": [
"12×5/4+9",
"12×5-9×4"
],
"4,5,9,13": [
"5×4+13-9",
"(13-9)×5+4"
],
"4,5,10,10": [
"10×10/5+4",
"(10/10+5)×4"
],
"4,5,10,11": [
"10×4-11-5",
"(11+5-10)×4"
],
"4,5,10,12": [
"12×5×4/10",
"(4-10/5)×12"
],
"4,5,10,13": [
"13+10+5-4"
],
"4,5,11,11": [
"(11-4)×5-11",
"(11/11+5)×4"
],
"4,5,11,12": [
"(11-5-4)×12",
"12+11+5-4",
"(12+5-11)×4"
],
"4,5,11,13": [
"(13+11)×(5-4)"
],
"4,5,12,12": [
"(12+12)×(5-4)",
"(5-12/4)×12",
"(12/12+5)×4"
],
"4,5,12,13": [
"13+12+4-5",
"(13-5)×12/4",
"(13+5-12)×4"
],
"4,5,13,13": [
"(13/13+5)×4"
],
"4,6,6,6": [
"6×4+6-6",
"6×6×4/6",
"(6+6)×(6-4)"
],
"4,6,6,7": [
"(7-6)×6×4",
"(7-4)×6+6",
"(7-6/6)×4"
],
"4,6,6,8": [
"8+6+6+4",
"8×6-6×4",
"8×6/(6-4)",
"6×6-8-4",
"(6+6)×8/4",
"(6-8/4)×6",
"(4-6/6)×8"
],
"4,6,6,9": [
"(6-4)×9+6",
"9×4-6-6",
"(9-4)×6-6"
],
"4,6,6,10": [
"(10+6)×6/4"
],
"4,6,6,12": [
"(6-4)×6+12",
"12×6/4+6"
],
"4,6,7,7": [
"7+7+6+4",
"6×4+7-7",
"7×6×4/7"
],
"4,6,7,8": [
"(6+4-7)×8",
"(8-7)×6×4"
],
"4,6,7,9": [
"(9+7)×6/4"
],
"4,6,7,10": [
"(6-4)×7+10",
"7×4+6-10",
"(7-4)×10-6",
"(10-6)×7-4"
],
"4,6,7,12": [
"12×6/(7-4)",
"(7-12/4)×6"
],
"4,6,8,8": [
"6×4+8-8",
"8×6×4/8",
"(6-4)×8+8",
"(8+8)×6/4",
"(8+4)×(8-6)"
],
"4,6,8,9": [
"(9-8)×6×4",
"9×8/4+6",
"(4-8/6)×9"
],
"4,6,8,10": [
"(8-6)×10+4",
"(10-6)×4+8"
],
"4,6,8,12": [
"(6+4-8)×12",
"8×6/4+12",
"(8+4)×12/6",
"(12-6)×(8-4)",
"12×4/(8-6)",
"(6-12/4)×8",
"(8-12/6)×4"
],
"4,6,8,13": [
"(13-6-4)×8"
],
"4,6,9,9": [
"6×4+9-9",
"9×6×4/9"
],
"4,6,9,10": [
"(10-9)×6×4",
"10×6/4+9",
"10×6-9×4",
"(10×9+6)/4"
],
"4,6,9,12": [
"(12+4)×9/6",
"(12-4)×(9-6)",
"(9-6)×4+12"
],
"4,6,9,13": [
"13+9+6-4"
],
"4,6,10,10": [
"6×4+10-10",
"10×6×4/10",
"10×4-10-6",
"(10-4)×(10-6)"
],
"4,6,10,11": [
"(11-10)×6×4"
],
"4,6,10,12": [
"12+10+6-4",
"(10-4)×6-12",
"12×10/4-6",
"12×10/6+4"
],
"4,6,11,11": [
"6×4+11-11",
"11×6×4/11",
"11+11+6-4"
],
"4,6,11,12": [
"(12-11)×6×4"
],
"4,6,12,12": [
"(12-6-4)×12",
"6×4+12-12",
"12×6×4/12",
"12×6-12×4",
"(4-12/6)×12"
],
"4,6,12,13": [
"(13-12)×6×4"
],
"4,6,13,13": [
"6×4+13-13",
"13×6×4/13",
"13+13+4-6"
],
"4,7,7,7": [
"(7-7/7)×4"
],
"4,7,7,8": [
"(7+7-8)×4",
"(4-7/7)×8"
],
"4,7,7,11": [
"7×4+7-11",
"(11-7)×7-4"
],
"4,7,8,8": [
"(7+4-8)×8",
"8×7-8×4",
"(7-8/8)×4"
],
"4,7,8,9": [
"9×8/(7-4)",
"(8+4)×(9-7)",
"(8+7-9)×4"
],
"4,7,8,10": [
"8×7/4+10"
],
"4,7,8,11": [
"(11-7)×4+8"
],
"4,7,8,12": [
"7×4+8-12",
"(12-8)×7-4"
],
"4,7,8,13": [
"13+8+7-4",
"(13-7)×(8-4)"
],
"4,7,9,9": [
"(7-9/9)×4"
],
"4,7,9,10": [
"10×4-9-7",
"(9+7-10)×4",
"(9-7)×10+4"
],
"4,7,9,11": [
"(7-4)×11-9",
"(9-4)×7-11"
],
"4,7,9,12": [
"(7+4-9)×12",
"12+9+7-4",
"12×4/(9-7)"
],
"4,7,9,13": [
"7×4+9-13",
"(13-9)×7-4"
],
"4,7,10,10": [
"(7-10/10)×4"
],
"4,7,10,11": [
"11+10+7-4",
"(10-4)×(11-7)",
"(10+7-11)×4"
],
"4,7,10,12": [
"(10+4)×12/7",
"(12-4)×(10-7)",
"(10-7)×4+12"
],
"4,7,11,11": [
"(7-11/11)×4"
],
"4,7,11,12": [
"(11+7-12)×4"
],
"4,7,11,13": [
"11×4-13-7"
],
"4,7,12,12": [
"(7-4)×12-12",
"(12×7+12)/4",
"(7-12/12)×4"
],
"4,7,12,13": [
"(13-7-4)×12",
"(12+7-13)×4"
],
"4,7,13,13": [
"(7-13/13)×4"
],
"4,8,8,8": [
"(8-4)×8-8",
"8×8/4+8",
"(4-8/8)×8"
],
"4,8,8,9": [
"(8+4-9)×8"
],
"4,8,8,10": [
"(8+4)×(10-8)",
"10×4-8-8",
"8×8-10×4",
"(8+8-10)×4"
],
"4,8,8,11": [
"(11×8+8)/4"
],
"4,8,8,12": [
"12+8+8-4",
"12×8/(8-4)",
"(12-8)×4+8"
],
"4,8,8,13": [
"(13×8-8)/4"
],
"4,8,9,9": [
"(4-9/9)×8"
],
"4,8,9,10": [
"(9+4-10)×8"
],
"4,8,9,11": [
"(8+4)×(11-9)",
"11+9+8-4",
"(9+8-11)×4"
],
"4,8,9,12": [
"9×8×4/12",
"(8-4)×9-12",
"9×8-12×4"
],
"4,8,9,13": [
"8/4+13+9",
"(13-9)×4+8"
],
"4,8,10,10": [
"10+10+8-4",
"(10-8)×10+4",
"(4-10/10)×8"
],
"4,8,10,11": [
"(10+4-11)×8"
],
"4,8,10,12": [
"(8+4)×(12-10)",
"(8+4-10)×12",
"8/4+12+10",
"(10-4)×(12-8)",
"12×4/(10-8)",
"(10+8-12)×4"
],
"4,8,11,11": [
"8/4+11+11",
"(4-11/11)×8"
],
"4,8,11,12": [
"(11+4-12)×8",
"11×4-12-8",
"(12-4)×(11-8)",
"(11-8)×4+12"
],
"4,8,11,13": [
"(8+4)×(13-11)",
"(11+8-13)×4"
],
"4,8,12,12": [
"(12+4)×12/8",
"(4-12/12)×8"
],
"4,8,12,13": [
"(12+4-13)×8",
"12/4+13+8"
],
"4,8,13,13": [
"13+13-8/4",
"(4-13/13)×8"
],
"4,9,9,10": [
"10+9+9-4"
],
"4,9,9,12": [
"(9+9-12)×4",
"(4-12/9)×9"
],
"4,9,10,11": [
"(11-9)×10+4"
],
"4,9,10,12": [
"12×10/(9-4)"
],
"4,9,10,13": [
"(10-4)×(13-9)",
"(10+9-13)×4"
],
"4,9,11,11": [
"11×4-11-9"
],
"4,9,11,12": [
"(9+4-11)×12",
"12×11/4-9",
"12×4/(11-9)"
],
"4,9,12,12": [
"(12-4)×(12-9)",
"12/4+12+9",
"(12×9-12)/4",
"(12-9)×4+12"
],
"4,10,10,11": [
"11×4-10-10"
],
"4,10,10,12": [
"(12-10)×10+4"
],
"4,10,11,12": [
"12/4+11+10"
],
"4,10,11,13": [
"(13-11)×10+4"
],
"4,10,12,12": [
"(10+4-12)×12",
"12×12/(10-4)",
"12×4/(12-10)"
],
"4,10,12,13": [
"(12-4)×(13-10)",
"(13-10)×4+12"
],
"4,11,12,13": [
"(11+4-13)×12",
"12×4-13-11",
"12×4/(13-11)"
],
"4,12,12,12": [
"12×4-12-12",
"12×12/4-12"
],
"5,5,5,5": [
"5×5-5/5"
],
"5,5,5,6": [
"5×5+5-6",
"(5-5/5)×6"
],
"5,5,5,9": [
"9+5+5+5"
],
"5,5,5,12": [
"(5+5)×12/5"
],
"5,5,6,6": [
"(5+5-6)×6",
"5×5-6/6",
"(6-6/5)×5"
],
"5,5,6,7": [
"5×5+6-7",
"7×5-6-5"
],
"5,5,6,8": [
"8+6+5+5"
],
"5,5,6,11": [
"6×5+5-11",
"(11-5)×5-6"
],
"5,5,7,7": [
"7+7+5+5",
"7×7-5×5",
"5×5-7/7",
"(7+5)×(7-5)"
],
"5,5,7,8": [
"(5+5-7)×8",
"5×5+7-8"
],
"5,5,7,10": [
"(7+5)×10/5"
],
"5,5,7,11": [
"(7-11/5)×5"
],
"5,5,8,8": [
"5×5-8/8"
],
"5,5,8,9": [
"5×5+8-9",
"(8-5)×5+9"
],
"5,5,8,10": [
"(10+5)×8/5",
"(5-10/5)×8"
],
"5,5,8,11": [
"8×5-11-5"
],
"5,5,8,12": [
"(5+5-8)×12"
],
"5,5,8,13": [
"(13-5-5)×8",
"(13-5)×(8-5)"
],
"5,5,9,9": [
"5×5-9/9"
],
"5,5,9,10": [
"5×5+9-10"
],
"5,5,9,11": [
"(11-5)×(9-5)"
],
"5,5,10,10": [
"5×5-10/10"
],
"5,5,10,11": [
"5×5+10-11"
],
"5,5,10,13": [
"5/5+13+10",
"(5-13/5)×10"
],
"5,5,11,11": [
"5×5-11/11"
],
"5,5,11,12": [
"5×5+11-12",
"5/5+12+11",
"(12-5)×5-11"
],
"5,5,11,13": [
"13+11+5-5",
"(13+11)×5/5"
],
"5,5,12,12": [
"(12-5-5)×12",
"5×5-12/12",
"12+12+5-5",
"(12+12)×5/5"
],
"5,5,12,13": [
"5×5+12-13",
"13+12-5/5"
],
"5,5,13,13": [
"5×5-13/13"
],
"5,6,6,6": [
"(5-6/6)×6"
],
"5,6,6,7": [
"7+6+6+5",
"(6+5-7)×6",
"6×6-7-5",
"(6+6)×(7-5)"
],
"5,6,6,8": [
"(8-5)×6+6"
],
"5,6,6,9": [
"9×6-6×5"
],
"5,6,6,10": [
"(10-5)×6-6",
"(6+6)×10/5",
"(6-10/5)×6"
],
"5,6,6,12": [
"6×5+6-12",
"12×5-6×6",
"(12-6)×5-6"
],
"5,6,7,7": [
"(5-7/7)×6"
],
"5,6,7,8": [
"(7+5)×(8-6)",
"(7+5-8)×6",
"8×6/(7-5)"
],
"5,6,7,9": [
"(7-5)×9+6"
],
"5,6,7,12": [
"(7+5)×12/6",
"(7-5)×6+12"
],
"5,6,7,13": [
"6×5+7-13",
"(13+7)×6/5",
"7×6-13-5",
"(13-7)×5-6"
],
"5,6,8,8": [
"(6+5-8)×8",
"(5-8/8)×6"
],
"5,6,8,9": [
"(8+5-9)×6",
"(9+6)×8/5"
],
"5,6,8,10": [
"8×6×5/10",
"8×5-10-6",
"(8-5)×10-6"
],
"5,6,8,12": [
"(12+8)×6/5",
"12×6/(8-5)",
"(5-12/6)×8"
],
"5,6,8,13": [
"(13+5)×8/6"
],
"5,6,9,9": [
"(9-6)×5+9",
"(5-9/9)×6"
],
"5,6,9,10": [
"(9+5-10)×6",
"10×9/5+6"
],
"5,6,9,11": [
"(11+9)×6/5",
"(11+5)×9/6"
],
"5,6,9,12": [
"(6+5-9)×12",
"(12-6)×(9-5)"
],
"5,6,9,13": [
"(13-5)×(9-6)"
],
"5,6,10,10": [
"(10+10)×6/5",
"(5-10/10)×6"
],
"5,6,10,11": [
"(10+5-11)×6",
"(11-5)×(10-6)"
],
"5,6,10,12": [
"10×6/5+12",
"(6-12/10)×5"
],
"5,6,10,13": [
"13+10+6-5"
],
"5,6,11,11": [
"(5-11/11)×6"
],
"5,6,11,12": [
"12+11+6-5",
"(11+5-12)×6",
"(11-5)×6-12"
],
"5,6,11,13": [
"(13+11)×(6-5)",
"(13-6)×5-11"
],
"5,6,12,12": [
"(12+12)×(6-5)",
"(5-12/12)×6"
],
"5,6,12,13": [
"(13-6-5)×12",
"13+12+5-6",
"(12+5-13)×6"
],
"5,6,13,13": [
"(5-13/13)×6"
],
"5,7,7,9": [
"(7+5)×(9-7)"
],
"5,7,7,10": [
"(7-5)×7+10"
],
"5,7,7,11": [
"(5-11/7)×7"
],
"5,7,8,8": [
"(7-5)×8+8",
"(8+7)×8/5"
],
"5,7,8,9": [
"(7+5-9)×8",
"8×5-9-7"
],
"5,7,8,10": [
"(7+5)×(10-8)"
],
"5,7,9,10": [
"(10-7)×5+9"
],
"5,7,9,11": [
"(7+5)×(11-9)"
],
"5,7,9,12": [
"(9+5)×12/7"
],
"5,7,9,13": [
"13+9+7-5",
"(13-7)×(9-5)"
],
"5,7,10,10": [
"10×7/5+10"
],
"5,7,10,11": [
"(10-5)×7-11"
],
"5,7,10,12": [
"(7+5)×(12-10)",
"(7+5-10)×12",
"12+10+7-5"
],
"5,7,10,13": [
"(13-5)×(10-7)"
],
"5,7,11,11": [
"11+11+7-5",
"(11-5)×(11-7)"
],
"5,7,11,13": [
"(7+5)×(13-11)"
],
"5,7,12,12": [
"12×7-12×5"
],
"5,7,13,13": [
"13+13+5-7"
],
"5,8,8,8": [
"8×5-8-8",
"8×8-8×5"
],
"5,8,8,9": [
"9×8/(8-5)",
"(9-5)×8-8"
],
"5,8,8,10": [
"(8+5-10)×8",
"10×8/5+8"
],
"5,8,8,13": [
"13+8+8-5"
],
"5,8,9,11": [
"(8-5)×11-9",
"(9+5-11)×8",
"(11-8)×5+9"
],
"5,8,9,12": [
"12+9+8-5",
"12×8/(9-5)"
],
"5,8,9,13": [
"9×5-13-8"
],
"5,8,10,11": [
"11+10+8-5"
],
"5,8,10,12": [
"(10+5-12)×8"
],
"5,8,11,12": [
"(8+5-11)×12",
"(11+5)×12/8",
"(11-5)×(12-8)"
],
"5,8,11,13": [
"(11+5-13)×8",
"(13-5)×(11-8)"
],
"5,8,12,12": [
"(8-5)×12-12"
],
"5,9,9,11": [
"11+9+9-5"
],
"5,9,9,12": [
"9×5-12-9",
"(9-5)×9-12",
"(12-9)×5+9"
],
"5,9,10,10": [
"10+10+9-5"
],
"5,9,10,11": [
"9×5-11-10"
],
"5,9,10,13": [
"10/5+13+9",
"(13-10)×5+9"
],
"5,9,11,13": [
"(11-5)×(13-9)"
],
"5,9,12,12": [
"(9+5-12)×12",
"(12×9+12)/5"
],
"5,9,12,13": [
"(13+5)×12/9",
"(13-5)×(12-9)"
],
"5,10,10,11": [
"(11×10+10)/5"
],
"5,10,10,12": [
"12×10/(10-5)",
"10/5+12+10"
],
"5,10,10,13": [
"(13×10-10)/5"
],
"5,10,11,11": [
"10/5+11+11"
],
"5,10,12,13": [
"(10+5-13)×12"
],
"5,10,13,13": [
"10×5-13-13",
"13+13-10/5",
"(13-5)×(13-10)"
],
"5,11,12,12": [
"12×12/(11-5)",
"(12×11-12)/5"
],
"6,6,6,6": [
"6+6+6+6",
"6×6-6-6"
],
"6,6,6,8": [
"(6+6)×(8-6)",
"(6+6-8)×6"
],
"6,6,6,9": [
"6×6×6/9",
"(9-6)×6+6"
],
"6,6,6,10": [
"10×6-6×6"
],
"6,6,6,11": [
"(11-6)×6-6"
],
"6,6,6,12": [
"(6+6)×12/6",
"(6-12/6)×6"
],
"6,6,7,9": [
"(6+6)×(9-7)",
"(7+6-9)×6"
],
"6,6,7,10": [
"(10-7)×6+6"
],
"6,6,7,11": [
"11×6-7×6"
],
"6,6,7,12": [
"7×6-12-6",
"(12-7)×6-6"
],
"6,6,8,8": [
"8×6/(8-6)"
],
"6,6,8,9": [
"(6+6-9)×8",
"(8-6)×9+6"
],
"6,6,8,10": [
"(6+6)×(10-8)",
"(8+6-10)×6"
],
"6,6,8,11": [
"(11-8)×6+6"
],
"6,6,8,12": [
"8×6×6/12",
"12×6-8×6",
"(8-6)×6+12",
"(12+6)×8/6"
],
"6,6,8,13": [
"(13-8)×6-6"
],
"6,6,9,10": [
"(9-6)×10-6",
"(10+6)×9/6"
],
"6,6,9,11": [
"(6+6)×(11-9)",
"(9+6-11)×6"
],
"6,6,9,12": [
"12×6/(9-6)",
"12×9/6+6",
"(12-9)×6+6"
],
"6,6,9,13": [
"13×6-9×6"
],
"6,6,10,12": [
"(6+6)×(12-10)",
"(6+6-10)×12",
"(10+6-12)×6",
"(12-6)×(10-6)"
],
"6,6,10,13": [
"6/6+13+10",
"(13-10)×6+6"
],
"6,6,11,12": [
"6/6+12+11"
],
"6,6,11,13": [
"(6+6)×(13-11)",
"13+11+6-6",
"(13+11)×6/6",
"(11+6-13)×6"
],
"6,6,12,12": [
"12+12+6-6",
"(12+12)×6/6",
"(12-6)×6-12"
],
"6,6,12,13": [
"13+12-6/6"
],
"6,7,7,10": [
"(7+7-10)×6"
],
"6,7,7,11": [
"7×6-11-7"
],
"6,7,8,9": [
"8×6/(9-7)"
],
"6,7,8,10": [
"(7+6-10)×8",
"7×6-10-8",
"(8-6)×7+10"
],
"6,7,8,11": [
"(11+7)×8/6",
"(8+7-11)×6"
],
"6,7,8,12": [
"(8+6)×12/7"
],
"6,7,9,9": [
"7×6-9-9",
"(9+7)×9/6",
"(9-7)×9+6"
],
"6,7,9,12": [
"(9+7-12)×6",
"(9-7)×6+12"
],
"6,7,10,10": [
"(10-7)×10-6"
],
"6,7,10,12": [
"12×7/6+10",
"12×7-10×6",
"12×6/(10-7)"
],
"6,7,10,13": [
"13+10+7-6",
"(13-7)×(10-6)",
"(10+7-13)×6"
],
"6,7,11,11": [
"(11-6)×7-11"
],
"6,7,11,12": [
"(7+6-11)×12",
"12+11+7-6",
"(12-6)×(11-7)"
],
"6,7,11,13": [
"(13+11)×(7-6)"
],
"6,7,12,12": [
"(12+12)×(7-6)"
],
"6,7,12,13": [
"13+12+6-7",
"(13-7)×6-12"
],
"6,8,8,8": [
"(8-6)×8+8"
],
"6,8,8,9": [
"9×8-8×6",
"(8+8)×9/6"
],
"6,8,8,10": [
"8×6/(10-8)",
"(10+8)×8/6",
"(10-6)×8-8"
],
"6,8,8,11": [
"(8+6-11)×8"
],
"6,8,8,12": [
"12×8/6+8",
"(8+8-12)×6"
],
"6,8,9,9": [
"(9+9)×8/6",
"9×8/(9-6)"
],
"6,8,9,10": [
"(10-8)×9+6"
],
"6,8,9,11": [
"8×6/(11-9)"
],
"6,8,9,12": [
"9×8/6+12",
"(9+6-12)×8"
],
"6,8,9,13": [
"13+9+8-6",
"(9+8-13)×6"
],
"6,8,10,11": [
"(11-8)×10-6"
],
"6,8,10,12": [
"8×6/(12-10)",
"12+10+8-6",
"(10+6)×12/8",
"12×8/(10-6)",
"(10-8)×6+12"
],
"6,8,10,13": [
"(10+6-13)×8"
],
"6,8,11,11": [
"11+11+8-6"
],
"6,8,11,12": [
"12×6/(11-8)"
],
"6,8,11,13": [
"8×6-13-11",
"8×6/(13-11)"
],
"6,8,12,12": [
"(8+6-12)×12",
"8×6-12-12",
"12×8-12×6",
"(12-6)×(12-8)",
"12×12/8+6"
],
"6,8,13,13": [
"13+13+6-8"
],
"6,9,9,10": [
"10×9/6+9"
],
"6,9,9,11": [
"(9-6)×11-9",
"(11-9)×9+6"
],
"6,9,9,12": [
"12+9+9-6"
],
"6,9,10,11": [
"11+10+9-6",
"10×9-11×6"
],
"6,9,10,12": [
"(10-6)×9-12",
"(12-9)×10-6",
"(12-10)×9+6"
],
"6,9,11,12": [
"(11-9)×6+12"
],
"6,9,11,13": [
"(13-11)×9+6"
],
"6,9,12,12": [
"(9-6)×12-12",
"(12+6)×12/9",
"12×6/(12-9)"
],
"6,9,12,13": [
"(9+6-13)×12",
"(12-6)×(13-9)",
"12/6+13+9"
],
"6,10,10,10": [
"10+10+10-6"
],
"6,10,10,13": [
"(13-10)×10-6"
],
"6,10,11,12": [
"12×10/(11-6)"
],
"6,10,12,12": [
"12/6+12+10",
"(12-10)×6+12"
],
"6,10,12,13": [
"12×6/(13-10)"
],
"6,11,11,12": [
"12/6+11+11"
],
"6,11,12,12": [
"(12×11+12)/6"
],
"6,11,12,13": [
"(13-11)×6+12"
],
"6,12,12,12": [
"12×12/(12-6)"
],
"6,12,12,13": [
"(13×12-12)/6"
],
"6,12,13,13": [
"13+13-12/6"
],
"7,7,7,12": [
"(7+7)×12/7"
],
"7,7,8,11": [
"(7+7-11)×8"
],
"7,7,9,10": [
"(9-7)×7+10"
],
"7,7,10,13": [
"7/7+13+10"
],
"7,7,11,12": [
"7/7+12+11",
"(12-7)×7-11"
],
"7,7,11,13": [
"13+11+7-7",
"(13+11)×7/7",
"(13-7)×(11-7)"
],
"7,7,12,12": [
"(7+7-12)×12",
"12+12+7-7",
"(12+12)×7/7"
],
"7,7,12,13": [
"7×7-13-12",
"13+12-7/7"
],
"7,8,8,9": [
"(9-7)×8+8"
],
"7,8,8,10": [
"10×8-8×7"
],
"7,8,8,11": [
"(11-7)×8-8"
],
"7,8,8,12": [
"(8+7-12)×8"
],
"7,8,8,13": [
"(13+8)×8/7"
],
"7,8,9,10": [
"9×8/(10-7)"
],
"7,8,9,12": [
"(12+9)×8/7",
"(9+7)×12/8"
],
"7,8,9,13": [
"(9+7-13)×8"
],
"7,8,10,10": [
"(10-8)×7+10"
],
"7,8,10,11": [
"(11+10)×8/7"
],
"7,8,10,13": [
"13+10+8-7"
],
"7,8,11,12": [
"12+11+8-7",
"12×8/(11-7)"
],
"7,8,11,13": [
"(13+11)×(8-7)",
"(13-8)×7-11"
],
"7,8,12,12": [
"(12+12)×(8-7)"
],
"7,8,12,13": [
"(8+7-13)×12",
"13+12+7-8",
"(13-7)×(12-8)"
],
"7,9,9,13": [
"13+9+9-7"
],
"7,9,10,11": [
"(10-7)×11-9",
"(11-9)×7+10"
],
"7,9,10,12": [
"12+10+9-7"
],
"7,9,11,11": [
"11+11+9-7"
],
"7,9,11,12": [
"(11+7)×12/9",
"(11-7)×9-12"
],
"7,9,12,12": [
"12×9-12×7"
],
"7,9,13,13": [
"13+13+7-9",
"(13-7)×(13-9)"
],
"7,10,10,11": [
"11+10+10-7"
],
"7,10,10,12": [
"(12-10)×7+10"
],
"7,10,11,13": [
"(13-11)×7+10"
],
"7,10,12,12": [
"(10-7)×12-12",
"12×10/(12-7)"
],
"7,10,12,13": [
"(13+7)×12/10"
],
"7,12,12,13": [
"12×12/(13-7)",
"(13×12+12)/7"
],
"8,8,8,10": [
"(10-8)×8+8"
],
"8,8,8,11": [
"11×8-8×8"
],
"8,8,8,12": [
"(8+8)×12/8",
"(12-8)×8-8"
],
"8,8,8,13": [
"(8+8-13)×8"
],
"8,8,9,11": [
"9×8/(11-8)",
"(11-9)×8+8"
],
"8,8,9,12": [
"12×8-9×8"
],
"8,8,9,13": [
"(13-9)×8-8"
],
"8,8,10,12": [
"(12-10)×8+8"
],
"8,8,10,13": [
"8/8+13+10",
"13×8-10×8"
],
"8,8,11,12": [
"8/8+12+11"
],
"8,8,11,13": [
"13+11+8-8",
"(13+11)×8/8",
"(13-11)×8+8"
],
"8,8,12,12": [
"12+12+8-8",
"(12+12)×8/8",
"12×8/(12-8)"
],
"8,8,12,13": [
"13+12-8/8"
],
"8,9,9,12": [
"9×8/(12-9)"
],
"8,9,10,12": [
"(10+8)×12/9",
"12×10/8+9"
],
"8,9,10,13": [
"9×8/(13-10)",
"13+10+9-8"
],
"8,9,11,11": [
"(11-8)×11-9"
],
"8,9,11,12": [
"12+11+9-8"
],
"8,9,11,13": [
"(13+11)×(9-8)"
],
"8,9,12,12": [
"(12+12)×(9-8)",
"(12-8)×9-12",
"12×12/9+8"
],
"8,9,12,13": [
"13+12+8-9",
"12×8/(13-9)"
],
"8,10,10,12": [
"12+10+10-8"
],
"8,10,11,11": [
"11+11+10-8"
],
"8,10,12,12": [
"(12+8)×12/10",
"12×10-12×8"
],
"8,10,12,13": [
"12×10/(13-8)"
],
"8,10,13,13": [
"13+13+8-10"
],
"8,11,12,12": [
"(11-8)×12-12"
],
"9,9,9,12": [
"(9+9)×12/9"
],
"9,9,10,13": [
"9/9+13+10"
],
"9,9,11,12": [
"9/9+12+11",
"(12-9)×11-9"
],
"9,9,11,13": [
"13+11+9-9",
"(13+11)×9/9"
],
"9,9,12,12": [
"12+12+9-9",
"(12+12)×9/9"
],
"9,9,12,13": [
"13+12-9/9",
"(13-9)×9-12"
],
"9,10,10,13": [
"13+10+10-9"
],
"9,10,11,12": [
"12+11+10-9",
"(11+9)×12/10"
],
"9,10,11,13": [
"(13+11)×(10-9)",
"(13-10)×11-9"
],
"9,10,12,12": [
"(12+12)×(10-9)"
],
"9,10,12,13": [
"13+12+9-10"
],
"9,11,11,11": [
"11+11+11-9"
],
"9,11,12,12": [
"12×11-12×9"
],
"9,11,12,13": [
"(13+9)×12/11"
],
"9,11,13,13": [
"13+13+9-11"
],
"9,12,12,12": [
"(12-9)×12-12"
],
"10,10,10,12": [
"(10+10)×12/10"
],
"10,10,10,13": [
"10/10+13+10"
],
"10,10,11,12": [
"10/10+12+11"
],
"10,10,11,13": [
"13+11+10-10",
"(13+11)×10/10"
],
"10,10,12,12": [
"12+12+10-10",
"(12+12)×10/10"
],
"10,10,12,13": [
"13+12-10/10"
],
"10,11,11,12": [
"12+11+11-10"
],
"10,11,11,13": [
"(13+11)×(11-10)",
"11/11+13+10"
],
"10,11,12,12": [
"(12+12)×(11-10)",
"(12+10)×12/11"
],
"10,11,12,13": [
"13+12+10-11"
],
"10,12,12,12": [
"12×12-12×10"
],
"10,12,12,13": [
"12/12+13+10",
"(13-10)×12-12"
],
"10,12,13,13": [
"13+13+10-12"
],
"10,13,13,13": [
"13/13+13+10"
],
"11,11,11,12": [
"(11+11)×12/11",
"11/11+12+11"
],
"11,11,11,13": [
"13+11+11-11",
"(13+11)×11/11"
],
"11,11,12,12": [
"12+12+11-11",
"(12+12)×11/11"
],
"11,11,12,13": [
"13+12-11/11",
"(13+11)×(12-11)"
],
"11,12,12,12": [
"12/12+12+11",
"(12+12)×(12-11)"
],
"11,12,12,13": [
"13+12+11-12",
"13×12-12×11",
"(13+11)×12/12"
],
"11,12,13,13": [
"13/13+12+11",
"(13+11)×(13-12)"
],
"11,13,13,13": [
"13+13+11-13",
"(13+11)×13/13"
],
"12,12,12,12": [
"12+12+12-12",
"(12+12)×12/12"
],
"12,12,12,13": [
"(12+12)×(13-12)",
"13+12-12/12"
],
"12,12,13,13": [
"13+12+12-13",
"(12+12)×13/13"
],
"12,13,13,13": [
"13+12-13/13",
"(13+13)×12/13"
]
}
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