{"problem":{"name":"1, 2, 3 - Decomposition","description":{"content":"Given is a positive integer $N$. Consider a sequence of integers $A = (A_1, \\ldots, A_K)$ that satisfies the conditions below: *   $\\sum_{i=1}^K A_i = N$; *   each $A_i$ is a positive integer such th","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc123_c"},"statements":[{"statement_type":"Markdown","content":"Given is a positive integer $N$. Consider a sequence of integers $A = (A_1, \\ldots, A_K)$ that satisfies the conditions below:\n\n*   $\\sum_{i=1}^K A_i = N$;\n*   each $A_i$ is a positive integer such that every digit in its decimal notation is $1$, $2$, or $3$.\n\nFind the minimum possible value of $K$, that is, the number of elements in such a sequence $A$.\nProcess $T$ test cases per input file.\n\n## Constraints\n\n*   $1\\leq T\\leq 1000$\n*   $1\\leq N\\leq 10^{18}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$T$\n$\\text{case}_1$\n$\\text{case}_2$\n$\\vdots$\n$\\text{case}_T$\n\nEach case is in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc123_c","tags":[],"sample_group":[["5\n456\n10000\n123\n314\n91","2\n4\n1\n2\n4\n\nFor each $N$, one optimal $A$ is shown below.\n\n*   For $N = 456$: $A = (133, 323)$.\n*   For $N = 10000$: $A = (323, 3132, 3232, 3313)$.\n*   For $N = 123$: $A = (123)$.\n*   For $N = 314$: $A = (312,2)$.\n*   For $N = 91$: $A = (22,23,23,23)$."]],"created_at":"2026-03-03 11:01:14"}}