{"problem":{"name":"Ex - E or m","description":{"content":"We have a grid $A$ with $N$ rows and $M$ columns. Initially, $0$ is written on every square.   Let us perform the following operation. *   For each integer $i$ such that $1 \\le i \\le N$, in the $i$\\-","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc295_h"},"statements":[{"statement_type":"Markdown","content":"We have a grid $A$ with $N$ rows and $M$ columns. Initially, $0$ is written on every square.  \nLet us perform the following operation.\n\n*   For each integer $i$ such that $1 \\le i \\le N$, in the $i$\\-th row, turn the digits in zero or more leftmost squares into $1$.\n*   For each integer $j$ such that $1 \\le j \\le M$, in the $j$\\-th column, turn the digits in zero or more topmost squares into $1$.\n\nLet $S$ be the set of grids that can be obtained in this way.\nYou are given a grid $X$ with $N$ rows and $M$ columns consisting of `0`, `1`, and `?`.  \nThere are $2^q$ grids that can be obtained by replacing each `?` with `0` or `1`, where $q$ is the number of `?` in $X$. How many of them are in $S$?  \nThis count can be enormous, so find it modulo $998244353$.\n\n## Constraints\n\n*   $N$ and $M$ are integers.\n*   $1 \\le N,M \\le 18$\n*   $X$ is a grid with $N$ rows and $M$ columns consisting of `0`, `1`, and `?`.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$X_{1,1} X_{1,2} \\dots X_{1,M}$\n$X_{2,1} X_{2,2} \\dots X_{2,M}$\n$\\vdots$\n$X_{N,1} X_{N,2} \\dots X_{N,M}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc295_h","tags":[],"sample_group":[["2 3\n0?1\n?1?","6\n\nThe following six grids are in $S$.\n\n011  011  001\n010  011  110\n\n001  011  011\n111  110  111"],["5 3\n101\n010\n101\n010\n101","0\n\n$X$ may have no `?`, and the answer may be $0$."],["18 18\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????\n??????????????????","462237431\n\nBe sure to find the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}