{"problem":{"name":"Count Strictly Increasing Sequences","description":{"content":"You are given a sequence $S_1,\\ldots,S_N$ of length-$M$ strings consisting of digits (`0123456789`) and `?`. There are $10^q$ ways to replace the occurrences of `?` with digits independently, where $q","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc292_g"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence $S_1,\\ldots,S_N$ of length-$M$ strings consisting of digits (`0123456789`) and `?`.\nThere are $10^q$ ways to replace the occurrences of `?` with digits independently, where $q$ is the total number of `?` in $S_1,\\ldots,S_N$. Among them, how many satisfy $S_1\\lt S_2 \\lt \\ldots \\lt S_N$ when the resulting strings are seen as integers? Find this count modulo $998244353$.\nThe resulting strings may have leading zeros. For instance, `0000000292` is seen as $292$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 40$\n*   $1 \\leq M \\leq 40$\n*   $N$ and $M$ are integers.\n*   $S_i$ is a string of length $M$ consisting of digits and `?`.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$S_1$\n$\\vdots$\n$S_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc292_g","tags":[],"sample_group":[["3 2\n?0\n??\n05","4\n\nHere are the four desired replacements.\n\n*   Replace the first character of $S_1$ with `0`, and the first and second characters of $S_2$ with `0` and `1`, respectively.\n*   Replace the first character of $S_1$ with `0`, and the first and second characters of $S_2$ with `0` and `2`, respectively.\n*   Replace the first character of $S_1$ with `0`, and the first and second characters of $S_2$ with `0` and `3`, respectively.\n*   Replace the first character of $S_1$ with `0`, and the first and second characters of $S_2$ with `0` and `4`, respectively."],["2 1\n0\n0","0"],["10 10\n1?22??37?4\n1??8?0??49\n3?02??8044\n51?4?8?7??\n5?9?20???2\n68?7?6?800\n?3??2???23\n?442312158\n??2??921?8\n????5?96??","137811792\n\nFind the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}