diff --git "a/data/math_operations/compositional_sft_n_steps_2/val_alpaca.jsonl" "b/data/math_operations/compositional_sft_n_steps_2/val_alpaca.jsonl"
new file mode 100644--- /dev/null
+++ "b/data/math_operations/compositional_sft_n_steps_2/val_alpaca.jsonl"
@@ -0,0 +1,200 @@
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(16143) + 41357)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 16143 are [1, 6, 1, 4, 3].\nRunning max: 1, 6, 6, 6, 6\nF(16143) = 1 + 6 + 6 + 6 + 6 = 25\n\n25 + 41357 = 41382\n\nThe digits of 41382 are [4, 1, 3, 8, 2].\n4 is not prime: 4\n1 is not prime: 1\n3 is prime: 3^2 = 9\n8 is not prime: 8\n2 is prime: 2^2 = 4\nD(41382) = 4 + 1 + 9 + 8 + 4 = 26\n\n\\boxed{26}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(48049) + 11717)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 48049 are [4, 8, 0, 4, 9].\nSum of digits = 4 + 8 + 0 + 4 + 9 = 25\nMax digit = 9\nA(48049) = 25 * 9 = 225\n\n225 + 11717 = 11942\n\nThe digits of 11942 are [1, 1, 9, 4, 2].\nRunning max: 1, 1, 9, 9, 9\nF(11942) = 1 + 1 + 9 + 9 + 9 = 29\n\n\\boxed{29}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(93206) + 81506)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93206 are [9, 3, 2, 0, 6].\nMin digit = 0\n(9 - 0)^2 = 81\n(3 - 0)^2 = 9\n(2 - 0)^2 = 4\n(0 - 0)^2 = 0\n(6 - 0)^2 = 36\nB(93206) = 81 + 9 + 4 + 0 + 36 = 130\n\n130 + 81506 = 81636\n\nThe digits of 81636 are [8, 1, 6, 3, 6].\nSum of digits = 8 + 1 + 6 + 3 + 6 = 24\nMax digit = 8\nA(81636) = 24 * 8 = 192\n\n\\boxed{192}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(4897) + 30641)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 4897 are [4, 8, 9, 7].\nT(4) = 4*5/2 = 10\nT(8) = 8*9/2 = 36\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nG(4897) = 10 + 36 + 45 + 28 = 119\n\n119 + 30641 = 30760\n\nThe digits of 30760 are [3, 0, 7, 6, 0].\nRunning max: 3, 3, 7, 7, 7\nF(30760) = 3 + 3 + 7 + 7 + 7 = 27\n\n\\boxed{27}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(49177) + 20537)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 49177 are [4, 9, 1, 7, 7].\n4 is not prime: 4\n9 is not prime: 9\n1 is not prime: 1\n7 is prime: 7^2 = 49\n7 is prime: 7^2 = 49\nD(49177) = 4 + 9 + 1 + 49 + 49 = 112\n\n112 + 20537 = 20649\n\nThe digits of 20649 are [2, 0, 6, 4, 9].\nAlternating sum of squares = 2^2 - 0^2 + 6^2 - 4^2 + 9^2 = 4 - 0 + 36 - 16 + 81 = 105\nC(20649) = |105| = 105\n\n\\boxed{105}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(83928) + 51494)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 83928 are [8, 3, 9, 2, 8].\nAlternating sum of squares = 8^2 - 3^2 + 9^2 - 2^2 + 8^2 = 64 - 9 + 81 - 4 + 64 = 196\nC(83928) = |196| = 196\n\n196 + 51494 = 51690\n\nThe digits of 51690 are [5, 1, 6, 9, 0].\nReversed: [0, 9, 6, 1, 5]\n5*0 + 1*9 + 6*6 + 9*1 + 0*5 = 0 + 9 + 36 + 9 + 0 = 54\nE(51690) = 54\n\n\\boxed{54}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(33526) + 62428)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 33526 are [3, 3, 5, 2, 6].\nSum of digits = 3 + 3 + 5 + 2 + 6 = 19\nMax digit = 6\nA(33526) = 19 * 6 = 114\n\n114 + 62428 = 62542\n\nThe digits of 62542 are [6, 2, 5, 4, 2].\nReversed: [2, 4, 5, 2, 6]\n6*2 + 2*4 + 5*5 + 4*2 + 2*6 = 12 + 8 + 25 + 8 + 12 = 65\nE(62542) = 65\n\n\\boxed{65}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(70088) + 81732)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 70088 are [7, 0, 0, 8, 8].\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(8) = 8*9/2 = 36\nG(70088) = 28 + 0 + 0 + 36 + 36 = 100\n\n100 + 81732 = 81832\n\nThe digits of 81832 are [8, 1, 8, 3, 2].\nReversed: [2, 3, 8, 1, 8]\n8*2 + 1*3 + 8*8 + 3*1 + 2*8 = 16 + 3 + 64 + 3 + 16 = 102\nE(81832) = 102\n\n\\boxed{102}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(81675) + 19118)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81675 are [8, 1, 6, 7, 5].\nMin digit = 1\n(8 - 1)^2 = 49\n(1 - 1)^2 = 0\n(6 - 1)^2 = 25\n(7 - 1)^2 = 36\n(5 - 1)^2 = 16\nB(81675) = 49 + 0 + 25 + 36 + 16 = 126\n\n126 + 19118 = 19244\n\nThe digits of 19244 are [1, 9, 2, 4, 4].\n1 is not prime: 1\n9 is not prime: 9\n2 is prime: 2^2 = 4\n4 is not prime: 4\n4 is not prime: 4\nD(19244) = 1 + 9 + 4 + 4 + 4 = 22\n\n\\boxed{22}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(6368) + 27531)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6368 are [6, 3, 6, 8].\nAlternating sum of squares = 6^2 - 3^2 + 6^2 - 8^2 = 36 - 9 + 36 - 64 = -1\nC(6368) = |-1| = 1\n\n1 + 27531 = 27532\n\nThe digits of 27532 are [2, 7, 5, 3, 2].\nReversed: [2, 3, 5, 7, 2]\n2*2 + 7*3 + 5*5 + 3*7 + 2*2 = 4 + 21 + 25 + 21 + 4 = 75\nE(27532) = 75\n\n\\boxed{75}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(77846) + 37131)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 77846 are [7, 7, 8, 4, 6].\nReversed: [6, 4, 8, 7, 7]\n7*6 + 7*4 + 8*8 + 4*7 + 6*7 = 42 + 28 + 64 + 28 + 42 = 204\nE(77846) = 204\n\n204 + 37131 = 37335\n\nThe digits of 37335 are [3, 7, 3, 3, 5].\nAlternating sum of squares = 3^2 - 7^2 + 3^2 - 3^2 + 5^2 = 9 - 49 + 9 - 9 + 25 = -15\nC(37335) = |-15| = 15\n\n\\boxed{15}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(F(6286) + 31175)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6286 are [6, 2, 8, 6].\nRunning max: 6, 6, 8, 8\nF(6286) = 6 + 6 + 8 + 8 = 28\n\n28 + 31175 = 31203\n\nThe digits of 31203 are [3, 1, 2, 0, 3].\nMin digit = 0\n(3 - 0)^2 = 9\n(1 - 0)^2 = 1\n(2 - 0)^2 = 4\n(0 - 0)^2 = 0\n(3 - 0)^2 = 9\nB(31203) = 9 + 1 + 4 + 0 + 9 = 23\n\n\\boxed{23}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(86765) + 42938)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86765 are [8, 6, 7, 6, 5].\nSum of digits = 8 + 6 + 7 + 6 + 5 = 32\nMax digit = 8\nA(86765) = 32 * 8 = 256\n\n256 + 42938 = 43194\n\nThe digits of 43194 are [4, 3, 1, 9, 4].\n4 is not prime: 4\n3 is prime: 3^2 = 9\n1 is not prime: 1\n9 is not prime: 9\n4 is not prime: 4\nD(43194) = 4 + 9 + 1 + 9 + 4 = 27\n\n\\boxed{27}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(14170) + 28913)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 14170 is \"14170\".\nRotations: 14170, 41701, 17014, 70141, 1417\nH(14170) = min(14170, 41701, 17014, 70141, 1417) = 1417\n\n1417 + 28913 = 30330\n\nThe digits of 30330 are [3, 0, 3, 3, 0].\nAlternating sum of squares = 3^2 - 0^2 + 3^2 - 3^2 + 0^2 = 9 - 0 + 9 - 9 + 0 = 9\nC(30330) = |9| = 9\n\n\\boxed{9}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(85664) + 76863)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 85664 are [8, 5, 6, 6, 4].\nReversed: [4, 6, 6, 5, 8]\n8*4 + 5*6 + 6*6 + 6*5 + 4*8 = 32 + 30 + 36 + 30 + 32 = 160\nE(85664) = 160\n\n160 + 76863 = 77023\n\nThe digits of 77023 are [7, 7, 0, 2, 3].\n7 is prime: 7^2 = 49\n7 is prime: 7^2 = 49\n0 is not prime: 0\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\nD(77023) = 49 + 49 + 0 + 4 + 9 = 111\n\n\\boxed{111}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(2587) + 90334)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 2587 are [2, 5, 8, 7].\nMin digit = 2\n(2 - 2)^2 = 0\n(5 - 2)^2 = 9\n(8 - 2)^2 = 36\n(7 - 2)^2 = 25\nB(2587) = 0 + 9 + 36 + 25 = 70\n\n70 + 90334 = 90404\n\nThe digits of 90404 are [9, 0, 4, 0, 4].\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nG(90404) = 45 + 0 + 10 + 0 + 10 = 65\n\n\\boxed{65}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(6322) + 44544)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6322 are [6, 3, 2, 2].\n6 is not prime: 6\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\nD(6322) = 6 + 9 + 4 + 4 = 23\n\n23 + 44544 = 44567\n\nThe digits of 44567 are [4, 4, 5, 6, 7].\nAlternating sum of squares = 4^2 - 4^2 + 5^2 - 6^2 + 7^2 = 16 - 16 + 25 - 36 + 49 = 38\nC(44567) = |38| = 38\n\n\\boxed{38}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(90406) + 58482)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90406 are [9, 0, 4, 0, 6].\n9 is not prime: 9\n0 is not prime: 0\n4 is not prime: 4\n0 is not prime: 0\n6 is not prime: 6\nD(90406) = 9 + 0 + 4 + 0 + 6 = 19\n\n19 + 58482 = 58501\n\nThe digit string of 58501 is \"58501\".\nRotations: 58501, 85015, 50158, 1585, 15850\nH(58501) = min(58501, 85015, 50158, 1585, 15850) = 1585\n\n\\boxed{1585}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(15176) + 95169)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 15176 are [1, 5, 1, 7, 6].\nRunning max: 1, 5, 5, 7, 7\nF(15176) = 1 + 5 + 5 + 7 + 7 = 25\n\n25 + 95169 = 95194\n\nThe digits of 95194 are [9, 5, 1, 9, 4].\nAlternating sum of squares = 9^2 - 5^2 + 1^2 - 9^2 + 4^2 = 81 - 25 + 1 - 81 + 16 = -8\nC(95194) = |-8| = 8\n\n\\boxed{8}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(58237) + 41919)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 58237 are [5, 8, 2, 3, 7].\nMin digit = 2\n(5 - 2)^2 = 9\n(8 - 2)^2 = 36\n(2 - 2)^2 = 0\n(3 - 2)^2 = 1\n(7 - 2)^2 = 25\nB(58237) = 9 + 36 + 0 + 1 + 25 = 71\n\n71 + 41919 = 41990\n\nThe digits of 41990 are [4, 1, 9, 9, 0].\nAlternating sum of squares = 4^2 - 1^2 + 9^2 - 9^2 + 0^2 = 16 - 1 + 81 - 81 + 0 = 15\nC(41990) = |15| = 15\n\n\\boxed{15}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(49840) + 78350)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 49840 are [4, 9, 8, 4, 0].\nRunning max: 4, 9, 9, 9, 9\nF(49840) = 4 + 9 + 9 + 9 + 9 = 40\n\n40 + 78350 = 78390\n\nThe digit string of 78390 is \"78390\".\nRotations: 78390, 83907, 39078, 90783, 7839\nH(78390) = min(78390, 83907, 39078, 90783, 7839) = 7839\n\n\\boxed{7839}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(71733) + 63665)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 71733 are [7, 1, 7, 3, 3].\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nG(71733) = 28 + 1 + 28 + 6 + 6 = 69\n\n69 + 63665 = 63734\n\nThe digits of 63734 are [6, 3, 7, 3, 4].\nAlternating sum of squares = 6^2 - 3^2 + 7^2 - 3^2 + 4^2 = 36 - 9 + 49 - 9 + 16 = 83\nC(63734) = |83| = 83\n\n\\boxed{83}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(C(33126) + 91868)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 33126 are [3, 3, 1, 2, 6].\nAlternating sum of squares = 3^2 - 3^2 + 1^2 - 2^2 + 6^2 = 9 - 9 + 1 - 4 + 36 = 33\nC(33126) = |33| = 33\n\n33 + 91868 = 91901\n\nThe digits of 91901 are [9, 1, 9, 0, 1].\nMin digit = 0\n(9 - 0)^2 = 81\n(1 - 0)^2 = 1\n(9 - 0)^2 = 81\n(0 - 0)^2 = 0\n(1 - 0)^2 = 1\nB(91901) = 81 + 1 + 81 + 0 + 1 = 164\n\n\\boxed{164}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(62180) + 16864)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 62180 are [6, 2, 1, 8, 0].\nSum of digits = 6 + 2 + 1 + 8 + 0 = 17\nMax digit = 8\nA(62180) = 17 * 8 = 136\n\n136 + 16864 = 17000\n\nThe digits of 17000 are [1, 7, 0, 0, 0].\n1 is not prime: 1\n7 is prime: 7^2 = 49\n0 is not prime: 0\n0 is not prime: 0\n0 is not prime: 0\nD(17000) = 1 + 49 + 0 + 0 + 0 = 50\n\n\\boxed{50}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(91995) + 2735)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 91995 are [9, 1, 9, 9, 5].\nReversed: [5, 9, 9, 1, 9]\n9*5 + 1*9 + 9*9 + 9*1 + 5*9 = 45 + 9 + 81 + 9 + 45 = 189\nE(91995) = 189\n\n189 + 2735 = 2924\n\nThe digits of 2924 are [2, 9, 2, 4].\nSum of digits = 2 + 9 + 2 + 4 = 17\nMax digit = 9\nA(2924) = 17 * 9 = 153\n\n\\boxed{153}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(20070) + 99256)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 20070 are [2, 0, 0, 7, 0].\nAlternating sum of squares = 2^2 - 0^2 + 0^2 - 7^2 + 0^2 = 4 - 0 + 0 - 49 + 0 = -45\nC(20070) = |-45| = 45\n\n45 + 99256 = 99301\n\nThe digits of 99301 are [9, 9, 3, 0, 1].\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nG(99301) = 45 + 45 + 6 + 0 + 1 = 97\n\n\\boxed{97}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(26934) + 43879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26934 are [2, 6, 9, 3, 4].\nAlternating sum of squares = 2^2 - 6^2 + 9^2 - 3^2 + 4^2 = 4 - 36 + 81 - 9 + 16 = 56\nC(26934) = |56| = 56\n\n56 + 43879 = 43935\n\nThe digits of 43935 are [4, 3, 9, 3, 5].\nRunning max: 4, 4, 9, 9, 9\nF(43935) = 4 + 4 + 9 + 9 + 9 = 35\n\n\\boxed{35}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(91120) + 91904)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 91120 are [9, 1, 1, 2, 0].\nSum of digits = 9 + 1 + 1 + 2 + 0 = 13\nMax digit = 9\nA(91120) = 13 * 9 = 117\n\n117 + 91904 = 92021\n\nThe digits of 92021 are [9, 2, 0, 2, 1].\nAlternating sum of squares = 9^2 - 2^2 + 0^2 - 2^2 + 1^2 = 81 - 4 + 0 - 4 + 1 = 74\nC(92021) = |74| = 74\n\n\\boxed{74}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(89881) + 74242)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 89881 are [8, 9, 8, 8, 1].\n8 is not prime: 8\n9 is not prime: 9\n8 is not prime: 8\n8 is not prime: 8\n1 is not prime: 1\nD(89881) = 8 + 9 + 8 + 8 + 1 = 34\n\n34 + 74242 = 74276\n\nThe digits of 74276 are [7, 4, 2, 7, 6].\nAlternating sum of squares = 7^2 - 4^2 + 2^2 - 7^2 + 6^2 = 49 - 16 + 4 - 49 + 36 = 24\nC(74276) = |24| = 24\n\n\\boxed{24}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(82616) + 78881)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 82616 are [8, 2, 6, 1, 6].\nAlternating sum of squares = 8^2 - 2^2 + 6^2 - 1^2 + 6^2 = 64 - 4 + 36 - 1 + 36 = 131\nC(82616) = |131| = 131\n\n131 + 78881 = 79012\n\nThe digit string of 79012 is \"79012\".\nRotations: 79012, 90127, 1279, 12790, 27901\nH(79012) = min(79012, 90127, 1279, 12790, 27901) = 1279\n\n\\boxed{1279}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(1219) + 86930)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 1219 are [1, 2, 1, 9].\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nG(1219) = 1 + 3 + 1 + 45 = 50\n\n50 + 86930 = 86980\n\nThe digits of 86980 are [8, 6, 9, 8, 0].\nAlternating sum of squares = 8^2 - 6^2 + 9^2 - 8^2 + 0^2 = 64 - 36 + 81 - 64 + 0 = 45\nC(86980) = |45| = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(39467) + 48050)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 39467 are [3, 9, 4, 6, 7].\nMin digit = 3\n(3 - 3)^2 = 0\n(9 - 3)^2 = 36\n(4 - 3)^2 = 1\n(6 - 3)^2 = 9\n(7 - 3)^2 = 16\nB(39467) = 0 + 36 + 1 + 9 + 16 = 62\n\n62 + 48050 = 48112\n\nThe digits of 48112 are [4, 8, 1, 1, 2].\nAlternating sum of squares = 4^2 - 8^2 + 1^2 - 1^2 + 2^2 = 16 - 64 + 1 - 1 + 4 = -44\nC(48112) = |-44| = 44\n\n\\boxed{44}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(55164) + 23312)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 55164 are [5, 5, 1, 6, 4].\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nG(55164) = 15 + 15 + 1 + 21 + 10 = 62\n\n62 + 23312 = 23374\n\nThe digits of 23374 are [2, 3, 3, 7, 4].\nAlternating sum of squares = 2^2 - 3^2 + 3^2 - 7^2 + 4^2 = 4 - 9 + 9 - 49 + 16 = -29\nC(23374) = |-29| = 29\n\n\\boxed{29}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(86725) + 58426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86725 are [8, 6, 7, 2, 5].\nMin digit = 2\n(8 - 2)^2 = 36\n(6 - 2)^2 = 16\n(7 - 2)^2 = 25\n(2 - 2)^2 = 0\n(5 - 2)^2 = 9\nB(86725) = 36 + 16 + 25 + 0 + 9 = 86\n\n86 + 58426 = 58512\n\nThe digits of 58512 are [5, 8, 5, 1, 2].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n1 is not prime: 1\n2 is prime: 2^2 = 4\nD(58512) = 25 + 8 + 25 + 1 + 4 = 63\n\n\\boxed{63}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(13235) + 4663)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13235 are [1, 3, 2, 3, 5].\nSum of digits = 1 + 3 + 2 + 3 + 5 = 14\nMax digit = 5\nA(13235) = 14 * 5 = 70\n\n70 + 4663 = 4733\n\nThe digits of 4733 are [4, 7, 3, 3].\nAlternating sum of squares = 4^2 - 7^2 + 3^2 - 3^2 = 16 - 49 + 9 - 9 = -33\nC(4733) = |-33| = 33\n\n\\boxed{33}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(86832) + 58002)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86832 are [8, 6, 8, 3, 2].\n8 is not prime: 8\n6 is not prime: 6\n8 is not prime: 8\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nD(86832) = 8 + 6 + 8 + 9 + 4 = 35\n\n35 + 58002 = 58037\n\nThe digits of 58037 are [5, 8, 0, 3, 7].\nAlternating sum of squares = 5^2 - 8^2 + 0^2 - 3^2 + 7^2 = 25 - 64 + 0 - 9 + 49 = 1\nC(58037) = |1| = 1\n\n\\boxed{1}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(68197) + 64384)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 68197 is \"68197\".\nRotations: 68197, 81976, 19768, 97681, 76819\nH(68197) = min(68197, 81976, 19768, 97681, 76819) = 19768\n\n19768 + 64384 = 84152\n\nThe digits of 84152 are [8, 4, 1, 5, 2].\nReversed: [2, 5, 1, 4, 8]\n8*2 + 4*5 + 1*1 + 5*4 + 2*8 = 16 + 20 + 1 + 20 + 16 = 73\nE(84152) = 73\n\n\\boxed{73}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(35386) + 70744)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 35386 are [3, 5, 3, 8, 6].\n3 is prime: 3^2 = 9\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n8 is not prime: 8\n6 is not prime: 6\nD(35386) = 9 + 25 + 9 + 8 + 6 = 57\n\n57 + 70744 = 70801\n\nThe digit string of 70801 is \"70801\".\nRotations: 70801, 8017, 80170, 1708, 17080\nH(70801) = min(70801, 8017, 80170, 1708, 17080) = 1708\n\n\\boxed{1708}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(81631) + 93262)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81631 are [8, 1, 6, 3, 1].\nSum of digits = 8 + 1 + 6 + 3 + 1 = 19\nMax digit = 8\nA(81631) = 19 * 8 = 152\n\n152 + 93262 = 93414\n\nThe digits of 93414 are [9, 3, 4, 1, 4].\nRunning max: 9, 9, 9, 9, 9\nF(93414) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(79381) + 28010)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 79381 are [7, 9, 3, 8, 1].\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nT(1) = 1*2/2 = 1\nG(79381) = 28 + 45 + 6 + 36 + 1 = 116\n\n116 + 28010 = 28126\n\nThe digits of 28126 are [2, 8, 1, 2, 6].\nReversed: [6, 2, 1, 8, 2]\n2*6 + 8*2 + 1*1 + 2*8 + 6*2 = 12 + 16 + 1 + 16 + 12 = 57\nE(28126) = 57\n\n\\boxed{57}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(17978) + 10018)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 17978 are [1, 7, 9, 7, 8].\nRunning max: 1, 7, 9, 9, 9\nF(17978) = 1 + 7 + 9 + 9 + 9 = 35\n\n35 + 10018 = 10053\n\nThe digits of 10053 are [1, 0, 0, 5, 3].\nAlternating sum of squares = 1^2 - 0^2 + 0^2 - 5^2 + 3^2 = 1 - 0 + 0 - 25 + 9 = -15\nC(10053) = |-15| = 15\n\n\\boxed{15}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(54896) + 89584)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54896 are [5, 4, 8, 9, 6].\nAlternating sum of squares = 5^2 - 4^2 + 8^2 - 9^2 + 6^2 = 25 - 16 + 64 - 81 + 36 = 28\nC(54896) = |28| = 28\n\n28 + 89584 = 89612\n\nThe digits of 89612 are [8, 9, 6, 1, 2].\nRunning max: 8, 9, 9, 9, 9\nF(89612) = 8 + 9 + 9 + 9 + 9 = 44\n\n\\boxed{44}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(13751) + 34246)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13751 are [1, 3, 7, 5, 1].\nSum of digits = 1 + 3 + 7 + 5 + 1 = 17\nMax digit = 7\nA(13751) = 17 * 7 = 119\n\n119 + 34246 = 34365\n\nThe digits of 34365 are [3, 4, 3, 6, 5].\nAlternating sum of squares = 3^2 - 4^2 + 3^2 - 6^2 + 5^2 = 9 - 16 + 9 - 36 + 25 = -9\nC(34365) = |-9| = 9\n\n\\boxed{9}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(67054) + 24765)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 67054 are [6, 7, 0, 5, 4].\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nG(67054) = 21 + 28 + 0 + 15 + 10 = 74\n\n74 + 24765 = 24839\n\nThe digits of 24839 are [2, 4, 8, 3, 9].\nRunning max: 2, 4, 8, 8, 9\nF(24839) = 2 + 4 + 8 + 8 + 9 = 31\n\n\\boxed{31}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(94210) + 42799)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 94210 are [9, 4, 2, 1, 0].\nSum of digits = 9 + 4 + 2 + 1 + 0 = 16\nMax digit = 9\nA(94210) = 16 * 9 = 144\n\n144 + 42799 = 42943\n\nThe digits of 42943 are [4, 2, 9, 4, 3].\nAlternating sum of squares = 4^2 - 2^2 + 9^2 - 4^2 + 3^2 = 16 - 4 + 81 - 16 + 9 = 86\nC(42943) = |86| = 86\n\n\\boxed{86}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(80962) + 87680)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 80962 are [8, 0, 9, 6, 2].\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nG(80962) = 36 + 0 + 45 + 21 + 3 = 105\n\n105 + 87680 = 87785\n\nThe digit string of 87785 is \"87785\".\nRotations: 87785, 77858, 78587, 85877, 58778\nH(87785) = min(87785, 77858, 78587, 85877, 58778) = 58778\n\n\\boxed{58778}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(F(15431) + 38745)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 15431 are [1, 5, 4, 3, 1].\nRunning max: 1, 5, 5, 5, 5\nF(15431) = 1 + 5 + 5 + 5 + 5 = 21\n\n21 + 38745 = 38766\n\nThe digits of 38766 are [3, 8, 7, 6, 6].\nMin digit = 3\n(3 - 3)^2 = 0\n(8 - 3)^2 = 25\n(7 - 3)^2 = 16\n(6 - 3)^2 = 9\n(6 - 3)^2 = 9\nB(38766) = 0 + 25 + 16 + 9 + 9 = 59\n\n\\boxed{59}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(C(37054) + 77082)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 37054 are [3, 7, 0, 5, 4].\nAlternating sum of squares = 3^2 - 7^2 + 0^2 - 5^2 + 4^2 = 9 - 49 + 0 - 25 + 16 = -49\nC(37054) = |-49| = 49\n\n49 + 77082 = 77131\n\nThe digits of 77131 are [7, 7, 1, 3, 1].\n7 is prime: 7^2 = 49\n7 is prime: 7^2 = 49\n1 is not prime: 1\n3 is prime: 3^2 = 9\n1 is not prime: 1\nD(77131) = 49 + 49 + 1 + 9 + 1 = 109\n\n\\boxed{109}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(14943) + 74286)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14943 are [1, 4, 9, 4, 3].\nReversed: [3, 4, 9, 4, 1]\n1*3 + 4*4 + 9*9 + 4*4 + 3*1 = 3 + 16 + 81 + 16 + 3 = 119\nE(14943) = 119\n\n119 + 74286 = 74405\n\nThe digits of 74405 are [7, 4, 4, 0, 5].\n7 is prime: 7^2 = 49\n4 is not prime: 4\n4 is not prime: 4\n0 is not prime: 0\n5 is prime: 5^2 = 25\nD(74405) = 49 + 4 + 4 + 0 + 25 = 82\n\n\\boxed{82}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(13928) + 57155)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13928 are [1, 3, 9, 2, 8].\nReversed: [8, 2, 9, 3, 1]\n1*8 + 3*2 + 9*9 + 2*3 + 8*1 = 8 + 6 + 81 + 6 + 8 = 109\nE(13928) = 109\n\n109 + 57155 = 57264\n\nThe digits of 57264 are [5, 7, 2, 6, 4].\n5 is prime: 5^2 = 25\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n6 is not prime: 6\n4 is not prime: 4\nD(57264) = 25 + 49 + 4 + 6 + 4 = 88\n\n\\boxed{88}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(65239) + 71236)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 65239 are [6, 5, 2, 3, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(9) = 9*10/2 = 45\nG(65239) = 21 + 15 + 3 + 6 + 45 = 90\n\n90 + 71236 = 71326\n\nThe digits of 71326 are [7, 1, 3, 2, 6].\nRunning max: 7, 7, 7, 7, 7\nF(71326) = 7 + 7 + 7 + 7 + 7 = 35\n\n\\boxed{35}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(26037) + 65147)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26037 are [2, 6, 0, 3, 7].\nReversed: [7, 3, 0, 6, 2]\n2*7 + 6*3 + 0*0 + 3*6 + 7*2 = 14 + 18 + 0 + 18 + 14 = 64\nE(26037) = 64\n\n64 + 65147 = 65211\n\nThe digits of 65211 are [6, 5, 2, 1, 1].\nSum of digits = 6 + 5 + 2 + 1 + 1 = 15\nMax digit = 6\nA(65211) = 15 * 6 = 90\n\n\\boxed{90}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(79823) + 45082)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 79823 are [7, 9, 8, 2, 3].\nRunning max: 7, 9, 9, 9, 9\nF(79823) = 7 + 9 + 9 + 9 + 9 = 43\n\n43 + 45082 = 45125\n\nThe digits of 45125 are [4, 5, 1, 2, 5].\nAlternating sum of squares = 4^2 - 5^2 + 1^2 - 2^2 + 5^2 = 16 - 25 + 1 - 4 + 25 = 13\nC(45125) = |13| = 13\n\n\\boxed{13}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(26181) + 48227)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 26181 is \"26181\".\nRotations: 26181, 61812, 18126, 81261, 12618\nH(26181) = min(26181, 61812, 18126, 81261, 12618) = 12618\n\n12618 + 48227 = 60845\n\nThe digits of 60845 are [6, 0, 8, 4, 5].\nSum of digits = 6 + 0 + 8 + 4 + 5 = 23\nMax digit = 8\nA(60845) = 23 * 8 = 184\n\n\\boxed{184}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(34471) + 32350)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 34471 are [3, 4, 4, 7, 1].\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nG(34471) = 6 + 10 + 10 + 28 + 1 = 55\n\n55 + 32350 = 32405\n\nThe digits of 32405 are [3, 2, 4, 0, 5].\nSum of digits = 3 + 2 + 4 + 0 + 5 = 14\nMax digit = 5\nA(32405) = 14 * 5 = 70\n\n\\boxed{70}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(68569) + 48845)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 68569 are [6, 8, 5, 6, 9].\nSum of digits = 6 + 8 + 5 + 6 + 9 = 34\nMax digit = 9\nA(68569) = 34 * 9 = 306\n\n306 + 48845 = 49151\n\nThe digits of 49151 are [4, 9, 1, 5, 1].\nRunning max: 4, 9, 9, 9, 9\nF(49151) = 4 + 9 + 9 + 9 + 9 = 40\n\n\\boxed{40}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(26433) + 81857)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26433 are [2, 6, 4, 3, 3].\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nG(26433) = 3 + 21 + 10 + 6 + 6 = 46\n\n46 + 81857 = 81903\n\nThe digits of 81903 are [8, 1, 9, 0, 3].\nSum of digits = 8 + 1 + 9 + 0 + 3 = 21\nMax digit = 9\nA(81903) = 21 * 9 = 189\n\n\\boxed{189}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(46913) + 19648)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 46913 are [4, 6, 9, 1, 3].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nG(46913) = 10 + 21 + 45 + 1 + 6 = 83\n\n83 + 19648 = 19731\n\nThe digit string of 19731 is \"19731\".\nRotations: 19731, 97311, 73119, 31197, 11973\nH(19731) = min(19731, 97311, 73119, 31197, 11973) = 11973\n\n\\boxed{11973}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(92200) + 28230)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 92200 are [9, 2, 2, 0, 0].\nSum of digits = 9 + 2 + 2 + 0 + 0 = 13\nMax digit = 9\nA(92200) = 13 * 9 = 117\n\n117 + 28230 = 28347\n\nThe digits of 28347 are [2, 8, 3, 4, 7].\n2 is prime: 2^2 = 4\n8 is not prime: 8\n3 is prime: 3^2 = 9\n4 is not prime: 4\n7 is prime: 7^2 = 49\nD(28347) = 4 + 8 + 9 + 4 + 49 = 74\n\n\\boxed{74}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(53707) + 60448)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 53707 is \"53707\".\nRotations: 53707, 37075, 70753, 7537, 75370\nH(53707) = min(53707, 37075, 70753, 7537, 75370) = 7537\n\n7537 + 60448 = 67985\n\nThe digits of 67985 are [6, 7, 9, 8, 5].\nRunning max: 6, 7, 9, 9, 9\nF(67985) = 6 + 7 + 9 + 9 + 9 = 40\n\n\\boxed{40}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(38712) + 65144)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 38712 are [3, 8, 7, 1, 2].\n3 is prime: 3^2 = 9\n8 is not prime: 8\n7 is prime: 7^2 = 49\n1 is not prime: 1\n2 is prime: 2^2 = 4\nD(38712) = 9 + 8 + 49 + 1 + 4 = 71\n\n71 + 65144 = 65215\n\nThe digits of 65215 are [6, 5, 2, 1, 5].\nReversed: [5, 1, 2, 5, 6]\n6*5 + 5*1 + 2*2 + 1*5 + 5*6 = 30 + 5 + 4 + 5 + 30 = 74\nE(65215) = 74\n\n\\boxed{74}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(21020) + 73922)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 21020 is \"21020\".\nRotations: 21020, 10202, 2021, 20210, 2102\nH(21020) = min(21020, 10202, 2021, 20210, 2102) = 2021\n\n2021 + 73922 = 75943\n\nThe digits of 75943 are [7, 5, 9, 4, 3].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n9 is not prime: 9\n4 is not prime: 4\n3 is prime: 3^2 = 9\nD(75943) = 49 + 25 + 9 + 4 + 9 = 96\n\n\\boxed{96}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(5164) + 19083)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 5164 are [5, 1, 6, 4].\nAlternating sum of squares = 5^2 - 1^2 + 6^2 - 4^2 = 25 - 1 + 36 - 16 = 44\nC(5164) = |44| = 44\n\n44 + 19083 = 19127\n\nThe digit string of 19127 is \"19127\".\nRotations: 19127, 91271, 12719, 27191, 71912\nH(19127) = min(19127, 91271, 12719, 27191, 71912) = 12719\n\n\\boxed{12719}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(71845) + 12016)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 71845 is \"71845\".\nRotations: 71845, 18457, 84571, 45718, 57184\nH(71845) = min(71845, 18457, 84571, 45718, 57184) = 18457\n\n18457 + 12016 = 30473\n\nThe digits of 30473 are [3, 0, 4, 7, 3].\nReversed: [3, 7, 4, 0, 3]\n3*3 + 0*7 + 4*4 + 7*0 + 3*3 = 9 + 0 + 16 + 0 + 9 = 34\nE(30473) = 34\n\n\\boxed{34}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(65058) + 6223)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 65058 are [6, 5, 0, 5, 8].\nAlternating sum of squares = 6^2 - 5^2 + 0^2 - 5^2 + 8^2 = 36 - 25 + 0 - 25 + 64 = 50\nC(65058) = |50| = 50\n\n50 + 6223 = 6273\n\nThe digits of 6273 are [6, 2, 7, 3].\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nG(6273) = 21 + 3 + 28 + 6 = 58\n\n\\boxed{58}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(27222) + 60459)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 27222 is \"27222\".\nRotations: 27222, 72222, 22227, 22272, 22722\nH(27222) = min(27222, 72222, 22227, 22272, 22722) = 22227\n\n22227 + 60459 = 82686\n\nThe digits of 82686 are [8, 2, 6, 8, 6].\nReversed: [6, 8, 6, 2, 8]\n8*6 + 2*8 + 6*6 + 8*2 + 6*8 = 48 + 16 + 36 + 16 + 48 = 164\nE(82686) = 164\n\n\\boxed{164}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(90204) + 8673)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90204 are [9, 0, 2, 0, 4].\nReversed: [4, 0, 2, 0, 9]\n9*4 + 0*0 + 2*2 + 0*0 + 4*9 = 36 + 0 + 4 + 0 + 36 = 76\nE(90204) = 76\n\n76 + 8673 = 8749\n\nThe digits of 8749 are [8, 7, 4, 9].\nAlternating sum of squares = 8^2 - 7^2 + 4^2 - 9^2 = 64 - 49 + 16 - 81 = -50\nC(8749) = |-50| = 50\n\n\\boxed{50}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(63001) + 22854)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 63001 are [6, 3, 0, 0, 1].\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nG(63001) = 21 + 6 + 0 + 0 + 1 = 28\n\n28 + 22854 = 22882\n\nThe digits of 22882 are [2, 2, 8, 8, 2].\nMin digit = 2\n(2 - 2)^2 = 0\n(2 - 2)^2 = 0\n(8 - 2)^2 = 36\n(8 - 2)^2 = 36\n(2 - 2)^2 = 0\nB(22882) = 0 + 0 + 36 + 36 + 0 = 72\n\n\\boxed{72}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(B(43332) + 81311)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 43332 are [4, 3, 3, 3, 2].\nMin digit = 2\n(4 - 2)^2 = 4\n(3 - 2)^2 = 1\n(3 - 2)^2 = 1\n(3 - 2)^2 = 1\n(2 - 2)^2 = 0\nB(43332) = 4 + 1 + 1 + 1 + 0 = 7\n\n7 + 81311 = 81318\n\nThe digit string of 81318 is \"81318\".\nRotations: 81318, 13188, 31881, 18813, 88131\nH(81318) = min(81318, 13188, 31881, 18813, 88131) = 13188\n\n\\boxed{13188}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(30737) + 91083)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 30737 are [3, 0, 7, 3, 7].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(7) = 7*8/2 = 28\nG(30737) = 6 + 0 + 28 + 6 + 28 = 68\n\n68 + 91083 = 91151\n\nThe digits of 91151 are [9, 1, 1, 5, 1].\nRunning max: 9, 9, 9, 9, 9\nF(91151) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(358) + 86392)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 358 is \"358\".\nRotations: 358, 583, 835\nH(358) = min(358, 583, 835) = 358\n\n358 + 86392 = 86750\n\nThe digits of 86750 are [8, 6, 7, 5, 0].\nSum of digits = 8 + 6 + 7 + 5 + 0 = 26\nMax digit = 8\nA(86750) = 26 * 8 = 208\n\n\\boxed{208}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(B(1671) + 56456)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 1671 are [1, 6, 7, 1].\nMin digit = 1\n(1 - 1)^2 = 0\n(6 - 1)^2 = 25\n(7 - 1)^2 = 36\n(1 - 1)^2 = 0\nB(1671) = 0 + 25 + 36 + 0 = 61\n\n61 + 56456 = 56517\n\nThe digit string of 56517 is \"56517\".\nRotations: 56517, 65175, 51756, 17565, 75651\nH(56517) = min(56517, 65175, 51756, 17565, 75651) = 17565\n\n\\boxed{17565}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(A(88032) + 97840)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88032 are [8, 8, 0, 3, 2].\nSum of digits = 8 + 8 + 0 + 3 + 2 = 21\nMax digit = 8\nA(88032) = 21 * 8 = 168\n\n168 + 97840 = 98008\n\nThe digit string of 98008 is \"98008\".\nRotations: 98008, 80089, 898, 8980, 89800\nH(98008) = min(98008, 80089, 898, 8980, 89800) = 898\n\n\\boxed{898}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(11665) + 44113)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 11665 are [1, 1, 6, 6, 5].\nReversed: [5, 6, 6, 1, 1]\n1*5 + 1*6 + 6*6 + 6*1 + 5*1 = 5 + 6 + 36 + 6 + 5 = 58\nE(11665) = 58\n\n58 + 44113 = 44171\n\nThe digits of 44171 are [4, 4, 1, 7, 1].\nRunning max: 4, 4, 4, 7, 7\nF(44171) = 4 + 4 + 4 + 7 + 7 = 26\n\n\\boxed{26}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(14474) + 69253)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14474 are [1, 4, 4, 7, 4].\nSum of digits = 1 + 4 + 4 + 7 + 4 = 20\nMax digit = 7\nA(14474) = 20 * 7 = 140\n\n140 + 69253 = 69393\n\nThe digits of 69393 are [6, 9, 3, 9, 3].\n6 is not prime: 6\n9 is not prime: 9\n3 is prime: 3^2 = 9\n9 is not prime: 9\n3 is prime: 3^2 = 9\nD(69393) = 6 + 9 + 9 + 9 + 9 = 42\n\n\\boxed{42}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(75255) + 4317)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 75255 are [7, 5, 2, 5, 5].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nG(75255) = 28 + 15 + 3 + 15 + 15 = 76\n\n76 + 4317 = 4393\n\nThe digits of 4393 are [4, 3, 9, 3].\nMin digit = 3\n(4 - 3)^2 = 1\n(3 - 3)^2 = 0\n(9 - 3)^2 = 36\n(3 - 3)^2 = 0\nB(4393) = 1 + 0 + 36 + 0 = 37\n\n\\boxed{37}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(F(87690) + 32025)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 87690 are [8, 7, 6, 9, 0].\nRunning max: 8, 8, 8, 9, 9\nF(87690) = 8 + 8 + 8 + 9 + 9 = 42\n\n42 + 32025 = 32067\n\nThe digits of 32067 are [3, 2, 0, 6, 7].\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nG(32067) = 6 + 3 + 0 + 21 + 28 = 58\n\n\\boxed{58}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(64763) + 44023)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 64763 are [6, 4, 7, 6, 3].\nSum of digits = 6 + 4 + 7 + 6 + 3 = 26\nMax digit = 7\nA(64763) = 26 * 7 = 182\n\n182 + 44023 = 44205\n\nThe digits of 44205 are [4, 4, 2, 0, 5].\nRunning max: 4, 4, 4, 4, 5\nF(44205) = 4 + 4 + 4 + 4 + 5 = 21\n\n\\boxed{21}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(19548) + 6641)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 19548 are [1, 9, 5, 4, 8].\nMin digit = 1\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(5 - 1)^2 = 16\n(4 - 1)^2 = 9\n(8 - 1)^2 = 49\nB(19548) = 0 + 64 + 16 + 9 + 49 = 138\n\n138 + 6641 = 6779\n\nThe digits of 6779 are [6, 7, 7, 9].\nAlternating sum of squares = 6^2 - 7^2 + 7^2 - 9^2 = 36 - 49 + 49 - 81 = -45\nC(6779) = |-45| = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(11807) + 21442)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 11807 is \"11807\".\nRotations: 11807, 18071, 80711, 7118, 71180\nH(11807) = min(11807, 18071, 80711, 7118, 71180) = 7118\n\n7118 + 21442 = 28560\n\nThe digits of 28560 are [2, 8, 5, 6, 0].\nMin digit = 0\n(2 - 0)^2 = 4\n(8 - 0)^2 = 64\n(5 - 0)^2 = 25\n(6 - 0)^2 = 36\n(0 - 0)^2 = 0\nB(28560) = 4 + 64 + 25 + 36 + 0 = 129\n\n\\boxed{129}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(67070) + 69263)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 67070 are [6, 7, 0, 7, 0].\nSum of digits = 6 + 7 + 0 + 7 + 0 = 20\nMax digit = 7\nA(67070) = 20 * 7 = 140\n\n140 + 69263 = 69403\n\nThe digits of 69403 are [6, 9, 4, 0, 3].\nReversed: [3, 0, 4, 9, 6]\n6*3 + 9*0 + 4*4 + 0*9 + 3*6 = 18 + 0 + 16 + 0 + 18 = 52\nE(69403) = 52\n\n\\boxed{52}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(9836) + 20063)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 9836 are [9, 8, 3, 6].\n9 is not prime: 9\n8 is not prime: 8\n3 is prime: 3^2 = 9\n6 is not prime: 6\nD(9836) = 9 + 8 + 9 + 6 = 32\n\n32 + 20063 = 20095\n\nThe digits of 20095 are [2, 0, 0, 9, 5].\nReversed: [5, 9, 0, 0, 2]\n2*5 + 0*9 + 0*0 + 9*0 + 5*2 = 10 + 0 + 0 + 0 + 10 = 20\nE(20095) = 20\n\n\\boxed{20}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(94840) + 33201)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 94840 are [9, 4, 8, 4, 0].\nAlternating sum of squares = 9^2 - 4^2 + 8^2 - 4^2 + 0^2 = 81 - 16 + 64 - 16 + 0 = 113\nC(94840) = |113| = 113\n\n113 + 33201 = 33314\n\nThe digits of 33314 are [3, 3, 3, 1, 4].\nSum of digits = 3 + 3 + 3 + 1 + 4 = 14\nMax digit = 4\nA(33314) = 14 * 4 = 56\n\n\\boxed{56}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(13276) + 21776)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13276 are [1, 3, 2, 7, 6].\nAlternating sum of squares = 1^2 - 3^2 + 2^2 - 7^2 + 6^2 = 1 - 9 + 4 - 49 + 36 = -17\nC(13276) = |-17| = 17\n\n17 + 21776 = 21793\n\nThe digits of 21793 are [2, 1, 7, 9, 3].\nReversed: [3, 9, 7, 1, 2]\n2*3 + 1*9 + 7*7 + 9*1 + 3*2 = 6 + 9 + 49 + 9 + 6 = 79\nE(21793) = 79\n\n\\boxed{79}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(33540) + 7267)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 33540 are [3, 3, 5, 4, 0].\nMin digit = 0\n(3 - 0)^2 = 9\n(3 - 0)^2 = 9\n(5 - 0)^2 = 25\n(4 - 0)^2 = 16\n(0 - 0)^2 = 0\nB(33540) = 9 + 9 + 25 + 16 + 0 = 59\n\n59 + 7267 = 7326\n\nThe digits of 7326 are [7, 3, 2, 6].\nRunning max: 7, 7, 7, 7\nF(7326) = 7 + 7 + 7 + 7 = 28\n\n\\boxed{28}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(84454) + 61022)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 84454 are [8, 4, 4, 5, 4].\n8 is not prime: 8\n4 is not prime: 4\n4 is not prime: 4\n5 is prime: 5^2 = 25\n4 is not prime: 4\nD(84454) = 8 + 4 + 4 + 25 + 4 = 45\n\n45 + 61022 = 61067\n\nThe digit string of 61067 is \"61067\".\nRotations: 61067, 10676, 6761, 67610, 76106\nH(61067) = min(61067, 10676, 6761, 67610, 76106) = 6761\n\n\\boxed{6761}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(30298) + 81588)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 30298 is \"30298\".\nRotations: 30298, 2983, 29830, 98302, 83029\nH(30298) = min(30298, 2983, 29830, 98302, 83029) = 2983\n\n2983 + 81588 = 84571\n\nThe digits of 84571 are [8, 4, 5, 7, 1].\nReversed: [1, 7, 5, 4, 8]\n8*1 + 4*7 + 5*5 + 7*4 + 1*8 = 8 + 28 + 25 + 28 + 8 = 97\nE(84571) = 97\n\n\\boxed{97}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(59867) + 20496)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59867 are [5, 9, 8, 6, 7].\nReversed: [7, 6, 8, 9, 5]\n5*7 + 9*6 + 8*8 + 6*9 + 7*5 = 35 + 54 + 64 + 54 + 35 = 242\nE(59867) = 242\n\n242 + 20496 = 20738\n\nThe digits of 20738 are [2, 0, 7, 3, 8].\nSum of digits = 2 + 0 + 7 + 3 + 8 = 20\nMax digit = 8\nA(20738) = 20 * 8 = 160\n\n\\boxed{160}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(38800) + 49933)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 38800 is \"38800\".\nRotations: 38800, 88003, 80038, 388, 3880\nH(38800) = min(38800, 88003, 80038, 388, 3880) = 388\n\n388 + 49933 = 50321\n\nThe digits of 50321 are [5, 0, 3, 2, 1].\nT(5) = 5*6/2 = 15\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nG(50321) = 15 + 0 + 6 + 3 + 1 = 25\n\n\\boxed{25}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(34619) + 65590)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 34619 are [3, 4, 6, 1, 9].\nAlternating sum of squares = 3^2 - 4^2 + 6^2 - 1^2 + 9^2 = 9 - 16 + 36 - 1 + 81 = 109\nC(34619) = |109| = 109\n\n109 + 65590 = 65699\n\nThe digits of 65699 are [6, 5, 6, 9, 9].\nRunning max: 6, 6, 6, 9, 9\nF(65699) = 6 + 6 + 6 + 9 + 9 = 36\n\n\\boxed{36}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(60853) + 50894)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 60853 is \"60853\".\nRotations: 60853, 8536, 85360, 53608, 36085\nH(60853) = min(60853, 8536, 85360, 53608, 36085) = 8536\n\n8536 + 50894 = 59430\n\nThe digits of 59430 are [5, 9, 4, 3, 0].\nAlternating sum of squares = 5^2 - 9^2 + 4^2 - 3^2 + 0^2 = 25 - 81 + 16 - 9 + 0 = -49\nC(59430) = |-49| = 49\n\n\\boxed{49}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(6564) + 51794)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6564 are [6, 5, 6, 4].\nSum of digits = 6 + 5 + 6 + 4 = 21\nMax digit = 6\nA(6564) = 21 * 6 = 126\n\n126 + 51794 = 51920\n\nThe digits of 51920 are [5, 1, 9, 2, 0].\nReversed: [0, 2, 9, 1, 5]\n5*0 + 1*2 + 9*9 + 2*1 + 0*5 = 0 + 2 + 81 + 2 + 0 = 85\nE(51920) = 85\n\n\\boxed{85}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(13082) + 54920)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 13082 is \"13082\".\nRotations: 13082, 30821, 8213, 82130, 21308\nH(13082) = min(13082, 30821, 8213, 82130, 21308) = 8213\n\n8213 + 54920 = 63133\n\nThe digits of 63133 are [6, 3, 1, 3, 3].\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nG(63133) = 21 + 6 + 1 + 6 + 6 = 40\n\n\\boxed{40}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(22898) + 15803)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 22898 is \"22898\".\nRotations: 22898, 28982, 89822, 98228, 82289\nH(22898) = min(22898, 28982, 89822, 98228, 82289) = 22898\n\n22898 + 15803 = 38701\n\nThe digits of 38701 are [3, 8, 7, 0, 1].\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nG(38701) = 6 + 36 + 28 + 0 + 1 = 71\n\n\\boxed{71}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(5170) + 73476)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 5170 is \"5170\".\nRotations: 5170, 1705, 7051, 517\nH(5170) = min(5170, 1705, 7051, 517) = 517\n\n517 + 73476 = 73993\n\nThe digits of 73993 are [7, 3, 9, 9, 3].\nAlternating sum of squares = 7^2 - 3^2 + 9^2 - 9^2 + 3^2 = 49 - 9 + 81 - 81 + 9 = 49\nC(73993) = |49| = 49\n\n\\boxed{49}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(38085) + 68386)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 38085 are [3, 8, 0, 8, 5].\nAlternating sum of squares = 3^2 - 8^2 + 0^2 - 8^2 + 5^2 = 9 - 64 + 0 - 64 + 25 = -94\nC(38085) = |-94| = 94\n\n94 + 68386 = 68480\n\nThe digit string of 68480 is \"68480\".\nRotations: 68480, 84806, 48068, 80684, 6848\nH(68480) = min(68480, 84806, 48068, 80684, 6848) = 6848\n\n\\boxed{6848}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(47214) + 76952)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 47214 are [4, 7, 2, 1, 4].\n4 is not prime: 4\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n4 is not prime: 4\nD(47214) = 4 + 49 + 4 + 1 + 4 = 62\n\n62 + 76952 = 77014\n\nThe digit string of 77014 is \"77014\".\nRotations: 77014, 70147, 1477, 14770, 47701\nH(77014) = min(77014, 70147, 1477, 14770, 47701) = 1477\n\n\\boxed{1477}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(88705) + 42190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 88705 is \"88705\".\nRotations: 88705, 87058, 70588, 5887, 58870\nH(88705) = min(88705, 87058, 70588, 5887, 58870) = 5887\n\n5887 + 42190 = 48077\n\nThe digits of 48077 are [4, 8, 0, 7, 7].\n4 is not prime: 4\n8 is not prime: 8\n0 is not prime: 0\n7 is prime: 7^2 = 49\n7 is prime: 7^2 = 49\nD(48077) = 4 + 8 + 0 + 49 + 49 = 110\n\n\\boxed{110}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(40987) + 8896)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 40987 is \"40987\".\nRotations: 40987, 9874, 98740, 87409, 74098\nH(40987) = min(40987, 9874, 98740, 87409, 74098) = 9874\n\n9874 + 8896 = 18770\n\nThe digits of 18770 are [1, 8, 7, 7, 0].\nMin digit = 0\n(1 - 0)^2 = 1\n(8 - 0)^2 = 64\n(7 - 0)^2 = 49\n(7 - 0)^2 = 49\n(0 - 0)^2 = 0\nB(18770) = 1 + 64 + 49 + 49 + 0 = 163\n\n\\boxed{163}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(55836) + 28445)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 55836 are [5, 5, 8, 3, 6].\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nG(55836) = 15 + 15 + 36 + 6 + 21 = 93\n\n93 + 28445 = 28538\n\nThe digits of 28538 are [2, 8, 5, 3, 8].\nSum of digits = 2 + 8 + 5 + 3 + 8 = 26\nMax digit = 8\nA(28538) = 26 * 8 = 208\n\n\\boxed{208}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(96801) + 68401)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 96801 is \"96801\".\nRotations: 96801, 68019, 80196, 1968, 19680\nH(96801) = min(96801, 68019, 80196, 1968, 19680) = 1968\n\n1968 + 68401 = 70369\n\nThe digits of 70369 are [7, 0, 3, 6, 9].\nReversed: [9, 6, 3, 0, 7]\n7*9 + 0*6 + 3*3 + 6*0 + 9*7 = 63 + 0 + 9 + 0 + 63 = 135\nE(70369) = 135\n\n\\boxed{135}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(A(15191) + 47915)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 15191 are [1, 5, 1, 9, 1].\nSum of digits = 1 + 5 + 1 + 9 + 1 = 17\nMax digit = 9\nA(15191) = 17 * 9 = 153\n\n153 + 47915 = 48068\n\nThe digit string of 48068 is \"48068\".\nRotations: 48068, 80684, 6848, 68480, 84806\nH(48068) = min(48068, 80684, 6848, 68480, 84806) = 6848\n\n\\boxed{6848}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(12451) + 40763)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 12451 are [1, 2, 4, 5, 1].\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nG(12451) = 1 + 3 + 10 + 15 + 1 = 30\n\n30 + 40763 = 40793\n\nThe digits of 40793 are [4, 0, 7, 9, 3].\nRunning max: 4, 4, 7, 9, 9\nF(40793) = 4 + 4 + 7 + 9 + 9 = 33\n\n\\boxed{33}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(99379) + 17962)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 99379 are [9, 9, 3, 7, 9].\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nG(99379) = 45 + 45 + 6 + 28 + 45 = 169\n\n169 + 17962 = 18131\n\nThe digit string of 18131 is \"18131\".\nRotations: 18131, 81311, 13118, 31181, 11813\nH(18131) = min(18131, 81311, 13118, 31181, 11813) = 11813\n\n\\boxed{11813}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(E(6014) + 23346)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6014 are [6, 0, 1, 4].\nReversed: [4, 1, 0, 6]\n6*4 + 0*1 + 1*0 + 4*6 = 24 + 0 + 0 + 24 = 48\nE(6014) = 48\n\n48 + 23346 = 23394\n\nThe digit string of 23394 is \"23394\".\nRotations: 23394, 33942, 39423, 94233, 42339\nH(23394) = min(23394, 33942, 39423, 94233, 42339) = 23394\n\n\\boxed{23394}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(D(18139) + 26331)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 18139 are [1, 8, 1, 3, 9].\n1 is not prime: 1\n8 is not prime: 8\n1 is not prime: 1\n3 is prime: 3^2 = 9\n9 is not prime: 9\nD(18139) = 1 + 8 + 1 + 9 + 9 = 28\n\n28 + 26331 = 26359\n\nThe digits of 26359 are [2, 6, 3, 5, 9].\nRunning max: 2, 6, 6, 6, 9\nF(26359) = 2 + 6 + 6 + 6 + 9 = 29\n\n\\boxed{29}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(86947) + 84122)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86947 are [8, 6, 9, 4, 7].\nMin digit = 4\n(8 - 4)^2 = 16\n(6 - 4)^2 = 4\n(9 - 4)^2 = 25\n(4 - 4)^2 = 0\n(7 - 4)^2 = 9\nB(86947) = 16 + 4 + 25 + 0 + 9 = 54\n\n54 + 84122 = 84176\n\nThe digits of 84176 are [8, 4, 1, 7, 6].\nAlternating sum of squares = 8^2 - 4^2 + 1^2 - 7^2 + 6^2 = 64 - 16 + 1 - 49 + 36 = 36\nC(84176) = |36| = 36\n\n\\boxed{36}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(84829) + 89994)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 84829 are [8, 4, 8, 2, 9].\nT(8) = 8*9/2 = 36\nT(4) = 4*5/2 = 10\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nG(84829) = 36 + 10 + 36 + 3 + 45 = 130\n\n130 + 89994 = 90124\n\nThe digits of 90124 are [9, 0, 1, 2, 4].\nSum of digits = 9 + 0 + 1 + 2 + 4 = 16\nMax digit = 9\nA(90124) = 16 * 9 = 144\n\n\\boxed{144}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(43078) + 73818)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 43078 are [4, 3, 0, 7, 8].\nReversed: [8, 7, 0, 3, 4]\n4*8 + 3*7 + 0*0 + 7*3 + 8*4 = 32 + 21 + 0 + 21 + 32 = 106\nE(43078) = 106\n\n106 + 73818 = 73924\n\nThe digits of 73924 are [7, 3, 9, 2, 4].\nAlternating sum of squares = 7^2 - 3^2 + 9^2 - 2^2 + 4^2 = 49 - 9 + 81 - 4 + 16 = 133\nC(73924) = |133| = 133\n\n\\boxed{133}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(46861) + 35172)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 46861 are [4, 6, 8, 6, 1].\nMin digit = 1\n(4 - 1)^2 = 9\n(6 - 1)^2 = 25\n(8 - 1)^2 = 49\n(6 - 1)^2 = 25\n(1 - 1)^2 = 0\nB(46861) = 9 + 25 + 49 + 25 + 0 = 108\n\n108 + 35172 = 35280\n\nThe digits of 35280 are [3, 5, 2, 8, 0].\n3 is prime: 3^2 = 9\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n0 is not prime: 0\nD(35280) = 9 + 25 + 4 + 8 + 0 = 46\n\n\\boxed{46}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(57372) + 36892)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 57372 is \"57372\".\nRotations: 57372, 73725, 37257, 72573, 25737\nH(57372) = min(57372, 73725, 37257, 72573, 25737) = 25737\n\n25737 + 36892 = 62629\n\nThe digits of 62629 are [6, 2, 6, 2, 9].\nRunning max: 6, 6, 6, 6, 9\nF(62629) = 6 + 6 + 6 + 6 + 9 = 33\n\n\\boxed{33}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(81501) + 12603)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81501 are [8, 1, 5, 0, 1].\n8 is not prime: 8\n1 is not prime: 1\n5 is prime: 5^2 = 25\n0 is not prime: 0\n1 is not prime: 1\nD(81501) = 8 + 1 + 25 + 0 + 1 = 35\n\n35 + 12603 = 12638\n\nThe digit string of 12638 is \"12638\".\nRotations: 12638, 26381, 63812, 38126, 81263\nH(12638) = min(12638, 26381, 63812, 38126, 81263) = 12638\n\n\\boxed{12638}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(35167) + 99532)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 35167 are [3, 5, 1, 6, 7].\nAlternating sum of squares = 3^2 - 5^2 + 1^2 - 6^2 + 7^2 = 9 - 25 + 1 - 36 + 49 = -2\nC(35167) = |-2| = 2\n\n2 + 99532 = 99534\n\nThe digits of 99534 are [9, 9, 5, 3, 4].\nSum of digits = 9 + 9 + 5 + 3 + 4 = 30\nMax digit = 9\nA(99534) = 30 * 9 = 270\n\n\\boxed{270}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(96084) + 57190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 96084 are [9, 6, 0, 8, 4].\n9 is not prime: 9\n6 is not prime: 6\n0 is not prime: 0\n8 is not prime: 8\n4 is not prime: 4\nD(96084) = 9 + 6 + 0 + 8 + 4 = 27\n\n27 + 57190 = 57217\n\nThe digit string of 57217 is \"57217\".\nRotations: 57217, 72175, 21757, 17572, 75721\nH(57217) = min(57217, 72175, 21757, 17572, 75721) = 17572\n\n\\boxed{17572}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(12183) + 32373)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 12183 are [1, 2, 1, 8, 3].\nSum of digits = 1 + 2 + 1 + 8 + 3 = 15\nMax digit = 8\nA(12183) = 15 * 8 = 120\n\n120 + 32373 = 32493\n\nThe digits of 32493 are [3, 2, 4, 9, 3].\nMin digit = 2\n(3 - 2)^2 = 1\n(2 - 2)^2 = 0\n(4 - 2)^2 = 4\n(9 - 2)^2 = 49\n(3 - 2)^2 = 1\nB(32493) = 1 + 0 + 4 + 49 + 1 = 55\n\n\\boxed{55}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(48840) + 19604)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 48840 is \"48840\".\nRotations: 48840, 88404, 84048, 40488, 4884\nH(48840) = min(48840, 88404, 84048, 40488, 4884) = 4884\n\n4884 + 19604 = 24488\n\nThe digits of 24488 are [2, 4, 4, 8, 8].\nMin digit = 2\n(2 - 2)^2 = 0\n(4 - 2)^2 = 4\n(4 - 2)^2 = 4\n(8 - 2)^2 = 36\n(8 - 2)^2 = 36\nB(24488) = 0 + 4 + 4 + 36 + 36 = 80\n\n\\boxed{80}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(C(44921) + 47576)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44921 are [4, 4, 9, 2, 1].\nAlternating sum of squares = 4^2 - 4^2 + 9^2 - 2^2 + 1^2 = 16 - 16 + 81 - 4 + 1 = 78\nC(44921) = |78| = 78\n\n78 + 47576 = 47654\n\nThe digits of 47654 are [4, 7, 6, 5, 4].\nMin digit = 4\n(4 - 4)^2 = 0\n(7 - 4)^2 = 9\n(6 - 4)^2 = 4\n(5 - 4)^2 = 1\n(4 - 4)^2 = 0\nB(47654) = 0 + 9 + 4 + 1 + 0 = 14\n\n\\boxed{14}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(23969) + 55507)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 23969 are [2, 3, 9, 6, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n9 is not prime: 9\n6 is not prime: 6\n9 is not prime: 9\nD(23969) = 4 + 9 + 9 + 6 + 9 = 37\n\n37 + 55507 = 55544\n\nThe digits of 55544 are [5, 5, 5, 4, 4].\nReversed: [4, 4, 5, 5, 5]\n5*4 + 5*4 + 5*5 + 4*5 + 4*5 = 20 + 20 + 25 + 20 + 20 = 105\nE(55544) = 105\n\n\\boxed{105}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(F(14920) + 91483)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14920 are [1, 4, 9, 2, 0].\nRunning max: 1, 4, 9, 9, 9\nF(14920) = 1 + 4 + 9 + 9 + 9 = 32\n\n32 + 91483 = 91515\n\nThe digits of 91515 are [9, 1, 5, 1, 5].\nReversed: [5, 1, 5, 1, 9]\n9*5 + 1*1 + 5*5 + 1*1 + 5*9 = 45 + 1 + 25 + 1 + 45 = 117\nE(91515) = 117\n\n\\boxed{117}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(52530) + 56377)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 52530 are [5, 2, 5, 3, 0].\nReversed: [0, 3, 5, 2, 5]\n5*0 + 2*3 + 5*5 + 3*2 + 0*5 = 0 + 6 + 25 + 6 + 0 = 37\nE(52530) = 37\n\n37 + 56377 = 56414\n\nThe digits of 56414 are [5, 6, 4, 1, 4].\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nG(56414) = 15 + 21 + 10 + 1 + 10 = 57\n\n\\boxed{57}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(52461) + 17958)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 52461 are [5, 2, 4, 6, 1].\nSum of digits = 5 + 2 + 4 + 6 + 1 = 18\nMax digit = 6\nA(52461) = 18 * 6 = 108\n\n108 + 17958 = 18066\n\nThe digits of 18066 are [1, 8, 0, 6, 6].\nRunning max: 1, 8, 8, 8, 8\nF(18066) = 1 + 8 + 8 + 8 + 8 = 33\n\n\\boxed{33}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(59839) + 96740)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59839 are [5, 9, 8, 3, 9].\nSum of digits = 5 + 9 + 8 + 3 + 9 = 34\nMax digit = 9\nA(59839) = 34 * 9 = 306\n\n306 + 96740 = 97046\n\nThe digits of 97046 are [9, 7, 0, 4, 6].\nMin digit = 0\n(9 - 0)^2 = 81\n(7 - 0)^2 = 49\n(0 - 0)^2 = 0\n(4 - 0)^2 = 16\n(6 - 0)^2 = 36\nB(97046) = 81 + 49 + 0 + 16 + 36 = 182\n\n\\boxed{182}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(35629) + 47642)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 35629 are [3, 5, 6, 2, 9].\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nG(35629) = 6 + 15 + 21 + 3 + 45 = 90\n\n90 + 47642 = 47732\n\nThe digits of 47732 are [4, 7, 7, 3, 2].\nMin digit = 2\n(4 - 2)^2 = 4\n(7 - 2)^2 = 25\n(7 - 2)^2 = 25\n(3 - 2)^2 = 1\n(2 - 2)^2 = 0\nB(47732) = 4 + 25 + 25 + 1 + 0 = 55\n\n\\boxed{55}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(50556) + 41811)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 50556 are [5, 0, 5, 5, 6].\nRunning max: 5, 5, 5, 5, 6\nF(50556) = 5 + 5 + 5 + 5 + 6 = 26\n\n26 + 41811 = 41837\n\nThe digit string of 41837 is \"41837\".\nRotations: 41837, 18374, 83741, 37418, 74183\nH(41837) = min(41837, 18374, 83741, 37418, 74183) = 18374\n\n\\boxed{18374}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(90426) + 86442)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90426 are [9, 0, 4, 2, 6].\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nG(90426) = 45 + 0 + 10 + 3 + 21 = 79\n\n79 + 86442 = 86521\n\nThe digits of 86521 are [8, 6, 5, 2, 1].\nSum of digits = 8 + 6 + 5 + 2 + 1 = 22\nMax digit = 8\nA(86521) = 22 * 8 = 176\n\n\\boxed{176}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(62684) + 11123)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 62684 are [6, 2, 6, 8, 4].\nReversed: [4, 8, 6, 2, 6]\n6*4 + 2*8 + 6*6 + 8*2 + 4*6 = 24 + 16 + 36 + 16 + 24 = 116\nE(62684) = 116\n\n116 + 11123 = 11239\n\nThe digits of 11239 are [1, 1, 2, 3, 9].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(9) = 9*10/2 = 45\nG(11239) = 1 + 1 + 3 + 6 + 45 = 56\n\n\\boxed{56}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(55278) + 83140)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 55278 are [5, 5, 2, 7, 8].\nSum of digits = 5 + 5 + 2 + 7 + 8 = 27\nMax digit = 8\nA(55278) = 27 * 8 = 216\n\n216 + 83140 = 83356\n\nThe digits of 83356 are [8, 3, 3, 5, 6].\nRunning max: 8, 8, 8, 8, 8\nF(83356) = 8 + 8 + 8 + 8 + 8 = 40\n\n\\boxed{40}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(85045) + 83998)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 85045 are [8, 5, 0, 4, 5].\nMin digit = 0\n(8 - 0)^2 = 64\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\n(4 - 0)^2 = 16\n(5 - 0)^2 = 25\nB(85045) = 64 + 25 + 0 + 16 + 25 = 130\n\n130 + 83998 = 84128\n\nThe digits of 84128 are [8, 4, 1, 2, 8].\nReversed: [8, 2, 1, 4, 8]\n8*8 + 4*2 + 1*1 + 2*4 + 8*8 = 64 + 8 + 1 + 8 + 64 = 145\nE(84128) = 145\n\n\\boxed{145}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(21860) + 85588)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 21860 are [2, 1, 8, 6, 0].\nAlternating sum of squares = 2^2 - 1^2 + 8^2 - 6^2 + 0^2 = 4 - 1 + 64 - 36 + 0 = 31\nC(21860) = |31| = 31\n\n31 + 85588 = 85619\n\nThe digits of 85619 are [8, 5, 6, 1, 9].\nSum of digits = 8 + 5 + 6 + 1 + 9 = 29\nMax digit = 9\nA(85619) = 29 * 9 = 261\n\n\\boxed{261}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(14818) + 95554)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14818 are [1, 4, 8, 1, 8].\nReversed: [8, 1, 8, 4, 1]\n1*8 + 4*1 + 8*8 + 1*4 + 8*1 = 8 + 4 + 64 + 4 + 8 = 88\nE(14818) = 88\n\n88 + 95554 = 95642\n\nThe digits of 95642 are [9, 5, 6, 4, 2].\nMin digit = 2\n(9 - 2)^2 = 49\n(5 - 2)^2 = 9\n(6 - 2)^2 = 16\n(4 - 2)^2 = 4\n(2 - 2)^2 = 0\nB(95642) = 49 + 9 + 16 + 4 + 0 = 78\n\n\\boxed{78}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(17368) + 9419)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 17368 are [1, 7, 3, 6, 8].\nAlternating sum of squares = 1^2 - 7^2 + 3^2 - 6^2 + 8^2 = 1 - 49 + 9 - 36 + 64 = -11\nC(17368) = |-11| = 11\n\n11 + 9419 = 9430\n\nThe digits of 9430 are [9, 4, 3, 0].\nRunning max: 9, 9, 9, 9\nF(9430) = 9 + 9 + 9 + 9 = 36\n\n\\boxed{36}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(95212) + 19863)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 95212 are [9, 5, 2, 1, 2].\nT(9) = 9*10/2 = 45\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nG(95212) = 45 + 15 + 3 + 1 + 3 = 67\n\n67 + 19863 = 19930\n\nThe digits of 19930 are [1, 9, 9, 3, 0].\nRunning max: 1, 9, 9, 9, 9\nF(19930) = 1 + 9 + 9 + 9 + 9 = 37\n\n\\boxed{37}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(7686) + 1649)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 7686 are [7, 6, 8, 6].\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(8) = 8*9/2 = 36\nT(6) = 6*7/2 = 21\nG(7686) = 28 + 21 + 36 + 21 = 106\n\n106 + 1649 = 1755\n\nThe digits of 1755 are [1, 7, 5, 5].\nSum of digits = 1 + 7 + 5 + 5 = 18\nMax digit = 7\nA(1755) = 18 * 7 = 126\n\n\\boxed{126}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(20892) + 78991)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 20892 are [2, 0, 8, 9, 2].\nReversed: [2, 9, 8, 0, 2]\n2*2 + 0*9 + 8*8 + 9*0 + 2*2 = 4 + 0 + 64 + 0 + 4 = 72\nE(20892) = 72\n\n72 + 78991 = 79063\n\nThe digits of 79063 are [7, 9, 0, 6, 3].\nSum of digits = 7 + 9 + 0 + 6 + 3 = 25\nMax digit = 9\nA(79063) = 25 * 9 = 225\n\n\\boxed{225}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(13593) + 85320)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13593 are [1, 3, 5, 9, 3].\nMin digit = 1\n(1 - 1)^2 = 0\n(3 - 1)^2 = 4\n(5 - 1)^2 = 16\n(9 - 1)^2 = 64\n(3 - 1)^2 = 4\nB(13593) = 0 + 4 + 16 + 64 + 4 = 88\n\n88 + 85320 = 85408\n\nThe digits of 85408 are [8, 5, 4, 0, 8].\nSum of digits = 8 + 5 + 4 + 0 + 8 = 25\nMax digit = 8\nA(85408) = 25 * 8 = 200\n\n\\boxed{200}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(54529) - 16505)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 54529 is \"54529\".\nRotations: 54529, 45295, 52954, 29545, 95452\nH(54529) = min(54529, 45295, 52954, 29545, 95452) = 29545\n\n29545 - 16505 = 13040\n\nThe digits of 13040 are [1, 3, 0, 4, 0].\nReversed: [0, 4, 0, 3, 1]\n1*0 + 3*4 + 0*0 + 4*3 + 0*1 = 0 + 12 + 0 + 12 + 0 = 24\nE(13040) = 24\n\n\\boxed{24}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(77430) + 62068)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 77430 are [7, 7, 4, 3, 0].\nT(7) = 7*8/2 = 28\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nG(77430) = 28 + 28 + 10 + 6 + 0 = 72\n\n72 + 62068 = 62140\n\nThe digits of 62140 are [6, 2, 1, 4, 0].\nMin digit = 0\n(6 - 0)^2 = 36\n(2 - 0)^2 = 4\n(1 - 0)^2 = 1\n(4 - 0)^2 = 16\n(0 - 0)^2 = 0\nB(62140) = 36 + 4 + 1 + 16 + 0 = 57\n\n\\boxed{57}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(63265) + 71920)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 63265 are [6, 3, 2, 6, 5].\nReversed: [5, 6, 2, 3, 6]\n6*5 + 3*6 + 2*2 + 6*3 + 5*6 = 30 + 18 + 4 + 18 + 30 = 100\nE(63265) = 100\n\n100 + 71920 = 72020\n\nThe digits of 72020 are [7, 2, 0, 2, 0].\nSum of digits = 7 + 2 + 0 + 2 + 0 = 11\nMax digit = 7\nA(72020) = 11 * 7 = 77\n\n\\boxed{77}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(D(74572) + 51828)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 74572 are [7, 4, 5, 7, 2].\n7 is prime: 7^2 = 49\n4 is not prime: 4\n5 is prime: 5^2 = 25\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\nD(74572) = 49 + 4 + 25 + 49 + 4 = 131\n\n131 + 51828 = 51959\n\nThe digits of 51959 are [5, 1, 9, 5, 9].\nMin digit = 1\n(5 - 1)^2 = 16\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(5 - 1)^2 = 16\n(9 - 1)^2 = 64\nB(51959) = 16 + 0 + 64 + 16 + 64 = 160\n\n\\boxed{160}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(88918) + 39967)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88918 are [8, 8, 9, 1, 8].\nReversed: [8, 1, 9, 8, 8]\n8*8 + 8*1 + 9*9 + 1*8 + 8*8 = 64 + 8 + 81 + 8 + 64 = 225\nE(88918) = 225\n\n225 + 39967 = 40192\n\nThe digits of 40192 are [4, 0, 1, 9, 2].\nAlternating sum of squares = 4^2 - 0^2 + 1^2 - 9^2 + 2^2 = 16 - 0 + 1 - 81 + 4 = -60\nC(40192) = |-60| = 60\n\n\\boxed{60}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(57430) + 54767)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 57430 are [5, 7, 4, 3, 0].\n5 is prime: 5^2 = 25\n7 is prime: 7^2 = 49\n4 is not prime: 4\n3 is prime: 3^2 = 9\n0 is not prime: 0\nD(57430) = 25 + 49 + 4 + 9 + 0 = 87\n\n87 + 54767 = 54854\n\nThe digit string of 54854 is \"54854\".\nRotations: 54854, 48545, 85454, 54548, 45485\nH(54854) = min(54854, 48545, 85454, 54548, 45485) = 45485\n\n\\boxed{45485}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(23758) + 37804)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 23758 are [2, 3, 7, 5, 8].\nMin digit = 2\n(2 - 2)^2 = 0\n(3 - 2)^2 = 1\n(7 - 2)^2 = 25\n(5 - 2)^2 = 9\n(8 - 2)^2 = 36\nB(23758) = 0 + 1 + 25 + 9 + 36 = 71\n\n71 + 37804 = 37875\n\nThe digits of 37875 are [3, 7, 8, 7, 5].\nReversed: [5, 7, 8, 7, 3]\n3*5 + 7*7 + 8*8 + 7*7 + 5*3 = 15 + 49 + 64 + 49 + 15 = 192\nE(37875) = 192\n\n\\boxed{192}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(80127) + 80589)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 80127 is \"80127\".\nRotations: 80127, 1278, 12780, 27801, 78012\nH(80127) = min(80127, 1278, 12780, 27801, 78012) = 1278\n\n1278 + 80589 = 81867\n\nThe digits of 81867 are [8, 1, 8, 6, 7].\nAlternating sum of squares = 8^2 - 1^2 + 8^2 - 6^2 + 7^2 = 64 - 1 + 64 - 36 + 49 = 140\nC(81867) = |140| = 140\n\n\\boxed{140}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(49774) + 52605)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 49774 is \"49774\".\nRotations: 49774, 97744, 77449, 74497, 44977\nH(49774) = min(49774, 97744, 77449, 74497, 44977) = 44977\n\n44977 + 52605 = 97582\n\nThe digits of 97582 are [9, 7, 5, 8, 2].\nReversed: [2, 8, 5, 7, 9]\n9*2 + 7*8 + 5*5 + 8*7 + 2*9 = 18 + 56 + 25 + 56 + 18 = 173\nE(97582) = 173\n\n\\boxed{173}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(47002) + 77235)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 47002 are [4, 7, 0, 0, 2].\nMin digit = 0\n(4 - 0)^2 = 16\n(7 - 0)^2 = 49\n(0 - 0)^2 = 0\n(0 - 0)^2 = 0\n(2 - 0)^2 = 4\nB(47002) = 16 + 49 + 0 + 0 + 4 = 69\n\n69 + 77235 = 77304\n\nThe digits of 77304 are [7, 7, 3, 0, 4].\nRunning max: 7, 7, 7, 7, 7\nF(77304) = 7 + 7 + 7 + 7 + 7 = 35\n\n\\boxed{35}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(A(80131) + 13907)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 80131 are [8, 0, 1, 3, 1].\nSum of digits = 8 + 0 + 1 + 3 + 1 = 13\nMax digit = 8\nA(80131) = 13 * 8 = 104\n\n104 + 13907 = 14011\n\nThe digits of 14011 are [1, 4, 0, 1, 1].\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nG(14011) = 1 + 10 + 0 + 1 + 1 = 13\n\n\\boxed{13}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(3777) + 12126)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 3777 are [3, 7, 7, 7].\nSum of digits = 3 + 7 + 7 + 7 = 24\nMax digit = 7\nA(3777) = 24 * 7 = 168\n\n168 + 12126 = 12294\n\nThe digits of 12294 are [1, 2, 2, 9, 4].\nAlternating sum of squares = 1^2 - 2^2 + 2^2 - 9^2 + 4^2 = 1 - 4 + 4 - 81 + 16 = -64\nC(12294) = |-64| = 64\n\n\\boxed{64}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(89714) + 82656)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 89714 are [8, 9, 7, 1, 4].\n8 is not prime: 8\n9 is not prime: 9\n7 is prime: 7^2 = 49\n1 is not prime: 1\n4 is not prime: 4\nD(89714) = 8 + 9 + 49 + 1 + 4 = 71\n\n71 + 82656 = 82727\n\nThe digits of 82727 are [8, 2, 7, 2, 7].\nReversed: [7, 2, 7, 2, 8]\n8*7 + 2*2 + 7*7 + 2*2 + 7*8 = 56 + 4 + 49 + 4 + 56 = 169\nE(82727) = 169\n\n\\boxed{169}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(95325) + 67216)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 95325 is \"95325\".\nRotations: 95325, 53259, 32595, 25953, 59532\nH(95325) = min(95325, 53259, 32595, 25953, 59532) = 25953\n\n25953 + 67216 = 93169\n\nThe digits of 93169 are [9, 3, 1, 6, 9].\n9 is not prime: 9\n3 is prime: 3^2 = 9\n1 is not prime: 1\n6 is not prime: 6\n9 is not prime: 9\nD(93169) = 9 + 9 + 1 + 6 + 9 = 34\n\n\\boxed{34}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(17125) + 39524)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 17125 are [1, 7, 1, 2, 5].\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nT(5) = 5*6/2 = 15\nG(17125) = 1 + 28 + 1 + 3 + 15 = 48\n\n48 + 39524 = 39572\n\nThe digits of 39572 are [3, 9, 5, 7, 2].\nReversed: [2, 7, 5, 9, 3]\n3*2 + 9*7 + 5*5 + 7*9 + 2*3 = 6 + 63 + 25 + 63 + 6 = 163\nE(39572) = 163\n\n\\boxed{163}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(63318) + 9303)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 63318 are [6, 3, 3, 1, 8].\nSum of digits = 6 + 3 + 3 + 1 + 8 = 21\nMax digit = 8\nA(63318) = 21 * 8 = 168\n\n168 + 9303 = 9471\n\nThe digits of 9471 are [9, 4, 7, 1].\nRunning max: 9, 9, 9, 9\nF(9471) = 9 + 9 + 9 + 9 = 36\n\n\\boxed{36}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(A(63979) + 31064)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 63979 are [6, 3, 9, 7, 9].\nSum of digits = 6 + 3 + 9 + 7 + 9 = 34\nMax digit = 9\nA(63979) = 34 * 9 = 306\n\n306 + 31064 = 31370\n\nThe digits of 31370 are [3, 1, 3, 7, 0].\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nG(31370) = 6 + 1 + 6 + 28 + 0 = 41\n\n\\boxed{41}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(14802) + 90743)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 14802 is \"14802\".\nRotations: 14802, 48021, 80214, 2148, 21480\nH(14802) = min(14802, 48021, 80214, 2148, 21480) = 2148\n\n2148 + 90743 = 92891\n\nThe digits of 92891 are [9, 2, 8, 9, 1].\nRunning max: 9, 9, 9, 9, 9\nF(92891) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(53907) + 29368)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 53907 are [5, 3, 9, 0, 7].\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(7) = 7*8/2 = 28\nG(53907) = 15 + 6 + 45 + 0 + 28 = 94\n\n94 + 29368 = 29462\n\nThe digits of 29462 are [2, 9, 4, 6, 2].\nReversed: [2, 6, 4, 9, 2]\n2*2 + 9*6 + 4*4 + 6*9 + 2*2 = 4 + 54 + 16 + 54 + 4 = 132\nE(29462) = 132\n\n\\boxed{132}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(57761) + 15382)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 57761 are [5, 7, 7, 6, 1].\nT(5) = 5*6/2 = 15\nT(7) = 7*8/2 = 28\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(1) = 1*2/2 = 1\nG(57761) = 15 + 28 + 28 + 21 + 1 = 93\n\n93 + 15382 = 15475\n\nThe digits of 15475 are [1, 5, 4, 7, 5].\nMin digit = 1\n(1 - 1)^2 = 0\n(5 - 1)^2 = 16\n(4 - 1)^2 = 9\n(7 - 1)^2 = 36\n(5 - 1)^2 = 16\nB(15475) = 0 + 16 + 9 + 36 + 16 = 77\n\n\\boxed{77}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(6025) + 31435)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6025 are [6, 0, 2, 5].\nReversed: [5, 2, 0, 6]\n6*5 + 0*2 + 2*0 + 5*6 = 30 + 0 + 0 + 30 = 60\nE(6025) = 60\n\n60 + 31435 = 31495\n\nThe digits of 31495 are [3, 1, 4, 9, 5].\nRunning max: 3, 3, 4, 9, 9\nF(31495) = 3 + 3 + 4 + 9 + 9 = 28\n\n\\boxed{28}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(C(8301) + 76531)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 8301 are [8, 3, 0, 1].\nAlternating sum of squares = 8^2 - 3^2 + 0^2 - 1^2 = 64 - 9 + 0 - 1 = 54\nC(8301) = |54| = 54\n\n54 + 76531 = 76585\n\nThe digits of 76585 are [7, 6, 5, 8, 5].\nMin digit = 5\n(7 - 5)^2 = 4\n(6 - 5)^2 = 1\n(5 - 5)^2 = 0\n(8 - 5)^2 = 9\n(5 - 5)^2 = 0\nB(76585) = 4 + 1 + 0 + 9 + 0 = 14\n\n\\boxed{14}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(34290) + 51341)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 34290 are [3, 4, 2, 9, 0].\nMin digit = 0\n(3 - 0)^2 = 9\n(4 - 0)^2 = 16\n(2 - 0)^2 = 4\n(9 - 0)^2 = 81\n(0 - 0)^2 = 0\nB(34290) = 9 + 16 + 4 + 81 + 0 = 110\n\n110 + 51341 = 51451\n\nThe digits of 51451 are [5, 1, 4, 5, 1].\nAlternating sum of squares = 5^2 - 1^2 + 4^2 - 5^2 + 1^2 = 25 - 1 + 16 - 25 + 1 = 16\nC(51451) = |16| = 16\n\n\\boxed{16}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(85848) + 74674)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 85848 are [8, 5, 8, 4, 8].\nRunning max: 8, 8, 8, 8, 8\nF(85848) = 8 + 8 + 8 + 8 + 8 = 40\n\n40 + 74674 = 74714\n\nThe digits of 74714 are [7, 4, 7, 1, 4].\nAlternating sum of squares = 7^2 - 4^2 + 7^2 - 1^2 + 4^2 = 49 - 16 + 49 - 1 + 16 = 97\nC(74714) = |97| = 97\n\n\\boxed{97}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(41187) + 19634)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 41187 are [4, 1, 1, 8, 7].\nReversed: [7, 8, 1, 1, 4]\n4*7 + 1*8 + 1*1 + 8*1 + 7*4 = 28 + 8 + 1 + 8 + 28 = 73\nE(41187) = 73\n\n73 + 19634 = 19707\n\nThe digits of 19707 are [1, 9, 7, 0, 7].\nMin digit = 0\n(1 - 0)^2 = 1\n(9 - 0)^2 = 81\n(7 - 0)^2 = 49\n(0 - 0)^2 = 0\n(7 - 0)^2 = 49\nB(19707) = 1 + 81 + 49 + 0 + 49 = 180\n\n\\boxed{180}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(88857) + 16278)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88857 are [8, 8, 8, 5, 7].\nSum of digits = 8 + 8 + 8 + 5 + 7 = 36\nMax digit = 8\nA(88857) = 36 * 8 = 288\n\n288 + 16278 = 16566\n\nThe digits of 16566 are [1, 6, 5, 6, 6].\nMin digit = 1\n(1 - 1)^2 = 0\n(6 - 1)^2 = 25\n(5 - 1)^2 = 16\n(6 - 1)^2 = 25\n(6 - 1)^2 = 25\nB(16566) = 0 + 25 + 16 + 25 + 25 = 91\n\n\\boxed{91}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(68788) - 17499)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 68788 is \"68788\".\nRotations: 68788, 87886, 78868, 88687, 86878\nH(68788) = min(68788, 87886, 78868, 88687, 86878) = 68788\n\n68788 - 17499 = 51289\n\nThe digits of 51289 are [5, 1, 2, 8, 9].\nSum of digits = 5 + 1 + 2 + 8 + 9 = 25\nMax digit = 9\nA(51289) = 25 * 9 = 225\n\n\\boxed{225}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(97468) - 39418)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 97468 is \"97468\".\nRotations: 97468, 74689, 46897, 68974, 89746\nH(97468) = min(97468, 74689, 46897, 68974, 89746) = 46897\n\n46897 - 39418 = 7479\n\nThe digits of 7479 are [7, 4, 7, 9].\nSum of digits = 7 + 4 + 7 + 9 = 27\nMax digit = 9\nA(7479) = 27 * 9 = 243\n\n\\boxed{243}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(94866) + 47042)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 94866 are [9, 4, 8, 6, 6].\nMin digit = 4\n(9 - 4)^2 = 25\n(4 - 4)^2 = 0\n(8 - 4)^2 = 16\n(6 - 4)^2 = 4\n(6 - 4)^2 = 4\nB(94866) = 25 + 0 + 16 + 4 + 4 = 49\n\n49 + 47042 = 47091\n\nThe digits of 47091 are [4, 7, 0, 9, 1].\nReversed: [1, 9, 0, 7, 4]\n4*1 + 7*9 + 0*0 + 9*7 + 1*4 = 4 + 63 + 0 + 63 + 4 = 134\nE(47091) = 134\n\n\\boxed{134}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(74057) + 78292)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 74057 are [7, 4, 0, 5, 7].\nMin digit = 0\n(7 - 0)^2 = 49\n(4 - 0)^2 = 16\n(0 - 0)^2 = 0\n(5 - 0)^2 = 25\n(7 - 0)^2 = 49\nB(74057) = 49 + 16 + 0 + 25 + 49 = 139\n\n139 + 78292 = 78431\n\nThe digits of 78431 are [7, 8, 4, 3, 1].\nAlternating sum of squares = 7^2 - 8^2 + 4^2 - 3^2 + 1^2 = 49 - 64 + 16 - 9 + 1 = -7\nC(78431) = |-7| = 7\n\n\\boxed{7}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(29358) + 70381)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 29358 is \"29358\".\nRotations: 29358, 93582, 35829, 58293, 82935\nH(29358) = min(29358, 93582, 35829, 58293, 82935) = 29358\n\n29358 + 70381 = 99739\n\nThe digits of 99739 are [9, 9, 7, 3, 9].\nReversed: [9, 3, 7, 9, 9]\n9*9 + 9*3 + 7*7 + 3*9 + 9*9 = 81 + 27 + 49 + 27 + 81 = 265\nE(99739) = 265\n\n\\boxed{265}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(G(87797) + 93454)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 87797 are [8, 7, 7, 9, 7].\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nG(87797) = 36 + 28 + 28 + 45 + 28 = 165\n\n165 + 93454 = 93619\n\nThe digits of 93619 are [9, 3, 6, 1, 9].\nRunning max: 9, 9, 9, 9, 9\nF(93619) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(44341) + 93382)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44341 are [4, 4, 3, 4, 1].\nRunning max: 4, 4, 4, 4, 4\nF(44341) = 4 + 4 + 4 + 4 + 4 = 20\n\n20 + 93382 = 93402\n\nThe digit string of 93402 is \"93402\".\nRotations: 93402, 34029, 40293, 2934, 29340\nH(93402) = min(93402, 34029, 40293, 2934, 29340) = 2934\n\n\\boxed{2934}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(68039) + 48716)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 68039 are [6, 8, 0, 3, 9].\nT(6) = 6*7/2 = 21\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(9) = 9*10/2 = 45\nG(68039) = 21 + 36 + 0 + 6 + 45 = 108\n\n108 + 48716 = 48824\n\nThe digits of 48824 are [4, 8, 8, 2, 4].\nAlternating sum of squares = 4^2 - 8^2 + 8^2 - 2^2 + 4^2 = 16 - 64 + 64 - 4 + 16 = 28\nC(48824) = |28| = 28\n\n\\boxed{28}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(68564) + 856)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 68564 is \"68564\".\nRotations: 68564, 85646, 56468, 64685, 46856\nH(68564) = min(68564, 85646, 56468, 64685, 46856) = 46856\n\n46856 + 856 = 47712\n\nThe digits of 47712 are [4, 7, 7, 1, 2].\nMin digit = 1\n(4 - 1)^2 = 9\n(7 - 1)^2 = 36\n(7 - 1)^2 = 36\n(1 - 1)^2 = 0\n(2 - 1)^2 = 1\nB(47712) = 9 + 36 + 36 + 0 + 1 = 82\n\n\\boxed{82}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(90209) + 4074)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90209 are [9, 0, 2, 0, 9].\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nT(9) = 9*10/2 = 45\nG(90209) = 45 + 0 + 3 + 0 + 45 = 93\n\n93 + 4074 = 4167\n\nThe digit string of 4167 is \"4167\".\nRotations: 4167, 1674, 6741, 7416\nH(4167) = min(4167, 1674, 6741, 7416) = 1674\n\n\\boxed{1674}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(91826) + 89856)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 91826 are [9, 1, 8, 2, 6].\nMin digit = 1\n(9 - 1)^2 = 64\n(1 - 1)^2 = 0\n(8 - 1)^2 = 49\n(2 - 1)^2 = 1\n(6 - 1)^2 = 25\nB(91826) = 64 + 0 + 49 + 1 + 25 = 139\n\n139 + 89856 = 89995\n\nThe digits of 89995 are [8, 9, 9, 9, 5].\nSum of digits = 8 + 9 + 9 + 9 + 5 = 40\nMax digit = 9\nA(89995) = 40 * 9 = 360\n\n\\boxed{360}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(81033) + 57319)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81033 are [8, 1, 0, 3, 3].\nRunning max: 8, 8, 8, 8, 8\nF(81033) = 8 + 8 + 8 + 8 + 8 = 40\n\n40 + 57319 = 57359\n\nThe digit string of 57359 is \"57359\".\nRotations: 57359, 73595, 35957, 59573, 95735\nH(57359) = min(57359, 73595, 35957, 59573, 95735) = 35957\n\n\\boxed{35957}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(12483) + 43089)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 12483 are [1, 2, 4, 8, 3].\nRunning max: 1, 2, 4, 8, 8\nF(12483) = 1 + 2 + 4 + 8 + 8 = 23\n\n23 + 43089 = 43112\n\nThe digits of 43112 are [4, 3, 1, 1, 2].\n4 is not prime: 4\n3 is prime: 3^2 = 9\n1 is not prime: 1\n1 is not prime: 1\n2 is prime: 2^2 = 4\nD(43112) = 4 + 9 + 1 + 1 + 4 = 19\n\n\\boxed{19}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(56734) + 3151)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 56734 are [5, 6, 7, 3, 4].\nMin digit = 3\n(5 - 3)^2 = 4\n(6 - 3)^2 = 9\n(7 - 3)^2 = 16\n(3 - 3)^2 = 0\n(4 - 3)^2 = 1\nB(56734) = 4 + 9 + 16 + 0 + 1 = 30\n\n30 + 3151 = 3181\n\nThe digits of 3181 are [3, 1, 8, 1].\n3 is prime: 3^2 = 9\n1 is not prime: 1\n8 is not prime: 8\n1 is not prime: 1\nD(3181) = 9 + 1 + 8 + 1 = 19\n\n\\boxed{19}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(86732) + 71225)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 86732 is \"86732\".\nRotations: 86732, 67328, 73286, 32867, 28673\nH(86732) = min(86732, 67328, 73286, 32867, 28673) = 28673\n\n28673 + 71225 = 99898\n\nThe digits of 99898 are [9, 9, 8, 9, 8].\nRunning max: 9, 9, 9, 9, 9\nF(99898) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(A(95243) + 6807)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 95243 are [9, 5, 2, 4, 3].\nSum of digits = 9 + 5 + 2 + 4 + 3 = 23\nMax digit = 9\nA(95243) = 23 * 9 = 207\n\n207 + 6807 = 7014\n\nThe digits of 7014 are [7, 0, 1, 4].\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nG(7014) = 28 + 0 + 1 + 10 = 39\n\n\\boxed{39}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(A(32581) + 11449)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 32581 are [3, 2, 5, 8, 1].\nSum of digits = 3 + 2 + 5 + 8 + 1 = 19\nMax digit = 8\nA(32581) = 19 * 8 = 152\n\n152 + 11449 = 11601\n\nThe digit string of 11601 is \"11601\".\nRotations: 11601, 16011, 60111, 1116, 11160\nH(11601) = min(11601, 16011, 60111, 1116, 11160) = 1116\n\n\\boxed{1116}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(63167) + 60667)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 63167 are [6, 3, 1, 6, 7].\nMin digit = 1\n(6 - 1)^2 = 25\n(3 - 1)^2 = 4\n(1 - 1)^2 = 0\n(6 - 1)^2 = 25\n(7 - 1)^2 = 36\nB(63167) = 25 + 4 + 0 + 25 + 36 = 90\n\n90 + 60667 = 60757\n\nThe digits of 60757 are [6, 0, 7, 5, 7].\nSum of digits = 6 + 0 + 7 + 5 + 7 = 25\nMax digit = 7\nA(60757) = 25 * 7 = 175\n\n\\boxed{175}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(F(45318) + 5913)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 45318 are [4, 5, 3, 1, 8].\nRunning max: 4, 5, 5, 5, 8\nF(45318) = 4 + 5 + 5 + 5 + 8 = 27\n\n27 + 5913 = 5940\n\nThe digits of 5940 are [5, 9, 4, 0].\nSum of digits = 5 + 9 + 4 + 0 = 18\nMax digit = 9\nA(5940) = 18 * 9 = 162\n\n\\boxed{162}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(86993) + 8753)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86993 are [8, 6, 9, 9, 3].\nAlternating sum of squares = 8^2 - 6^2 + 9^2 - 9^2 + 3^2 = 64 - 36 + 81 - 81 + 9 = 37\nC(86993) = |37| = 37\n\n37 + 8753 = 8790\n\nThe digits of 8790 are [8, 7, 9, 0].\nReversed: [0, 9, 7, 8]\n8*0 + 7*9 + 9*7 + 0*8 = 0 + 63 + 63 + 0 = 126\nE(8790) = 126\n\n\\boxed{126}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(F(88643) + 54622)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88643 are [8, 8, 6, 4, 3].\nRunning max: 8, 8, 8, 8, 8\nF(88643) = 8 + 8 + 8 + 8 + 8 = 40\n\n40 + 54622 = 54662\n\nThe digits of 54662 are [5, 4, 6, 6, 2].\nSum of digits = 5 + 4 + 6 + 6 + 2 = 23\nMax digit = 6\nA(54662) = 23 * 6 = 138\n\n\\boxed{138}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(D(84070) + 54296)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 84070 are [8, 4, 0, 7, 0].\n8 is not prime: 8\n4 is not prime: 4\n0 is not prime: 0\n7 is prime: 7^2 = 49\n0 is not prime: 0\nD(84070) = 8 + 4 + 0 + 49 + 0 = 61\n\n61 + 54296 = 54357\n\nThe digits of 54357 are [5, 4, 3, 5, 7].\nMin digit = 3\n(5 - 3)^2 = 4\n(4 - 3)^2 = 1\n(3 - 3)^2 = 0\n(5 - 3)^2 = 4\n(7 - 3)^2 = 16\nB(54357) = 4 + 1 + 0 + 4 + 16 = 25\n\n\\boxed{25}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(50446) + 25525)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 50446 is \"50446\".\nRotations: 50446, 4465, 44650, 46504, 65044\nH(50446) = min(50446, 4465, 44650, 46504, 65044) = 4465\n\n4465 + 25525 = 29990\n\nThe digits of 29990 are [2, 9, 9, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nG(29990) = 3 + 45 + 45 + 45 + 0 = 138\n\n\\boxed{138}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(19484) + 89069)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 19484 are [1, 9, 4, 8, 4].\nRunning max: 1, 9, 9, 9, 9\nF(19484) = 1 + 9 + 9 + 9 + 9 = 37\n\n37 + 89069 = 89106\n\nThe digits of 89106 are [8, 9, 1, 0, 6].\n8 is not prime: 8\n9 is not prime: 9\n1 is not prime: 1\n0 is not prime: 0\n6 is not prime: 6\nD(89106) = 8 + 9 + 1 + 0 + 6 = 24\n\n\\boxed{24}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(73183) + 11594)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 73183 are [7, 3, 1, 8, 3].\nReversed: [3, 8, 1, 3, 7]\n7*3 + 3*8 + 1*1 + 8*3 + 3*7 = 21 + 24 + 1 + 24 + 21 = 91\nE(73183) = 91\n\n91 + 11594 = 11685\n\nThe digits of 11685 are [1, 1, 6, 8, 5].\nAlternating sum of squares = 1^2 - 1^2 + 6^2 - 8^2 + 5^2 = 1 - 1 + 36 - 64 + 25 = -3\nC(11685) = |-3| = 3\n\n\\boxed{3}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(80335) + 60761)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 80335 are [8, 0, 3, 3, 5].\nReversed: [5, 3, 3, 0, 8]\n8*5 + 0*3 + 3*3 + 3*0 + 5*8 = 40 + 0 + 9 + 0 + 40 = 89\nE(80335) = 89\n\n89 + 60761 = 60850\n\nThe digits of 60850 are [6, 0, 8, 5, 0].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(0) = 0*1/2 = 0\nG(60850) = 21 + 0 + 36 + 15 + 0 = 72\n\n\\boxed{72}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(1526) + 48799)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 1526 are [1, 5, 2, 6].\nRunning max: 1, 5, 5, 6\nF(1526) = 1 + 5 + 5 + 6 = 17\n\n17 + 48799 = 48816\n\nThe digits of 48816 are [4, 8, 8, 1, 6].\nAlternating sum of squares = 4^2 - 8^2 + 8^2 - 1^2 + 6^2 = 16 - 64 + 64 - 1 + 36 = 51\nC(48816) = |51| = 51\n\n\\boxed{51}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(84331) + 22409)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 84331 are [8, 4, 3, 3, 1].\nT(8) = 8*9/2 = 36\nT(4) = 4*5/2 = 10\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nG(84331) = 36 + 10 + 6 + 6 + 1 = 59\n\n59 + 22409 = 22468\n\nThe digits of 22468 are [2, 2, 4, 6, 8].\nSum of digits = 2 + 2 + 4 + 6 + 8 = 22\nMax digit = 8\nA(22468) = 22 * 8 = 176\n\n\\boxed{176}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(20568) + 79852)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 20568 are [2, 0, 5, 6, 8].\nRunning max: 2, 2, 5, 6, 8\nF(20568) = 2 + 2 + 5 + 6 + 8 = 23\n\n23 + 79852 = 79875\n\nThe digit string of 79875 is \"79875\".\nRotations: 79875, 98757, 87579, 75798, 57987\nH(79875) = min(79875, 98757, 87579, 75798, 57987) = 57987\n\n\\boxed{57987}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(66265) + 14787)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 66265 are [6, 6, 2, 6, 5].\nSum of digits = 6 + 6 + 2 + 6 + 5 = 25\nMax digit = 6\nA(66265) = 25 * 6 = 150\n\n150 + 14787 = 14937\n\nThe digits of 14937 are [1, 4, 9, 3, 7].\n1 is not prime: 1\n4 is not prime: 4\n9 is not prime: 9\n3 is prime: 3^2 = 9\n7 is prime: 7^2 = 49\nD(14937) = 1 + 4 + 9 + 9 + 49 = 72\n\n\\boxed{72}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(61510) + 36220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 61510 are [6, 1, 5, 1, 0].\nT(6) = 6*7/2 = 21\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nG(61510) = 21 + 1 + 15 + 1 + 0 = 38\n\n38 + 36220 = 36258\n\nThe digit string of 36258 is \"36258\".\nRotations: 36258, 62583, 25836, 58362, 83625\nH(36258) = min(36258, 62583, 25836, 58362, 83625) = 25836\n\n\\boxed{25836}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(64990) + 46068)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 64990 are [6, 4, 9, 9, 0].\nMin digit = 0\n(6 - 0)^2 = 36\n(4 - 0)^2 = 16\n(9 - 0)^2 = 81\n(9 - 0)^2 = 81\n(0 - 0)^2 = 0\nB(64990) = 36 + 16 + 81 + 81 + 0 = 214\n\n214 + 46068 = 46282\n\nThe digits of 46282 are [4, 6, 2, 8, 2].\nAlternating sum of squares = 4^2 - 6^2 + 2^2 - 8^2 + 2^2 = 16 - 36 + 4 - 64 + 4 = -76\nC(46282) = |-76| = 76\n\n\\boxed{76}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(21679) + 34442)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 21679 are [2, 1, 6, 7, 9].\nRunning max: 2, 2, 6, 7, 9\nF(21679) = 2 + 2 + 6 + 7 + 9 = 26\n\n26 + 34442 = 34468\n\nThe digit string of 34468 is \"34468\".\nRotations: 34468, 44683, 46834, 68344, 83446\nH(34468) = min(34468, 44683, 46834, 68344, 83446) = 34468\n\n\\boxed{34468}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(B(9812) + 57211)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 9812 are [9, 8, 1, 2].\nMin digit = 1\n(9 - 1)^2 = 64\n(8 - 1)^2 = 49\n(1 - 1)^2 = 0\n(2 - 1)^2 = 1\nB(9812) = 64 + 49 + 0 + 1 = 114\n\n114 + 57211 = 57325\n\nThe digits of 57325 are [5, 7, 3, 2, 5].\nAlternating sum of squares = 5^2 - 7^2 + 3^2 - 2^2 + 5^2 = 25 - 49 + 9 - 4 + 25 = 6\nC(57325) = |6| = 6\n\n\\boxed{6}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(98491) + 60010)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 98491 are [9, 8, 4, 9, 1].\nMin digit = 1\n(9 - 1)^2 = 64\n(8 - 1)^2 = 49\n(4 - 1)^2 = 9\n(9 - 1)^2 = 64\n(1 - 1)^2 = 0\nB(98491) = 64 + 49 + 9 + 64 + 0 = 186\n\n186 + 60010 = 60196\n\nThe digits of 60196 are [6, 0, 1, 9, 6].\nReversed: [6, 9, 1, 0, 6]\n6*6 + 0*9 + 1*1 + 9*0 + 6*6 = 36 + 0 + 1 + 0 + 36 = 73\nE(60196) = 73\n\n\\boxed{73}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(64441) + 75752)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 64441 are [6, 4, 4, 4, 1].\nMin digit = 1\n(6 - 1)^2 = 25\n(4 - 1)^2 = 9\n(4 - 1)^2 = 9\n(4 - 1)^2 = 9\n(1 - 1)^2 = 0\nB(64441) = 25 + 9 + 9 + 9 + 0 = 52\n\n52 + 75752 = 75804\n\nThe digits of 75804 are [7, 5, 8, 0, 4].\nReversed: [4, 0, 8, 5, 7]\n7*4 + 5*0 + 8*8 + 0*5 + 4*7 = 28 + 0 + 64 + 0 + 28 = 120\nE(75804) = 120\n\n\\boxed{120}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(42026) + 58080)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 42026 is \"42026\".\nRotations: 42026, 20264, 2642, 26420, 64202\nH(42026) = min(42026, 20264, 2642, 26420, 64202) = 2642\n\n2642 + 58080 = 60722\n\nThe digits of 60722 are [6, 0, 7, 2, 2].\nSum of digits = 6 + 0 + 7 + 2 + 2 = 17\nMax digit = 7\nA(60722) = 17 * 7 = 119\n\n\\boxed{119}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(31574) + 97102)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 31574 are [3, 1, 5, 7, 4].\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nG(31574) = 6 + 1 + 15 + 28 + 10 = 60\n\n60 + 97102 = 97162\n\nThe digits of 97162 are [9, 7, 1, 6, 2].\nReversed: [2, 6, 1, 7, 9]\n9*2 + 7*6 + 1*1 + 6*7 + 2*9 = 18 + 42 + 1 + 42 + 18 = 121\nE(97162) = 121\n\n\\boxed{121}"}
+{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(43371) + 67612)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 43371 are [4, 3, 3, 7, 1].\n4 is not prime: 4\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n7 is prime: 7^2 = 49\n1 is not prime: 1\nD(43371) = 4 + 9 + 9 + 49 + 1 = 72\n\n72 + 67612 = 67684\n\nThe digit string of 67684 is \"67684\".\nRotations: 67684, 76846, 68467, 84676, 46768\nH(67684) = min(67684, 76846, 68467, 84676, 46768) = 46768\n\n\\boxed{46768}"}