{"problem":{"name":"Sum of Sum of Digits","description":{"content":"For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$. You are given a sequence of positive","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":5000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc153_d"},"statements":[{"statement_type":"Markdown","content":"For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$.\nYou are given a sequence of positive integers $A = (A_1, \\ldots, A_N)$. Find the minimum possible value of $\\sum_{i=1}^N f(A_i + x)$ where $x$ is a non-negative integer.\n\n## Constraints\n\n*   $1\\leq N\\leq 2\\times 10^5$\n*   $1\\leq A_i < 10^9$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc153_d","tags":[],"sample_group":[["4\n4 13 8 6","14\n\nFor instance, $x = 7$ makes $\\sum_{i=1}^N f(A_i+x) = f(11) + f(20) + f(15) + f(13) = 14$."],["4\n123 45 678 90","34\n\nFor instance, $x = 22$ makes $\\sum_{i=1}^N f(A_i+x) = f(145) + f(67) + f(700) + f(112) = 34$."],["3\n1 10 100","3\n\nFor instance, $x = 0$ makes $\\sum_{i=1}^N f(A_i+x) = f(1) + f(10) + f(100) = 3$."],["1\n153153153","1\n\nFor instance, $x = 9999846846847$ makes $\\sum_{i=1}^N f(A_i+x) = f(10000000000000) = 1$."]],"created_at":"2026-03-03 11:01:13"}}