{"problem":{"name":"Mex Mat","description":{"content":"Consider an $N \\times N$ matrix. Let us denote by $a_{i, j}$ the entry in the $i$\\-th row and $j$\\-th column. For $a_{i, j}$ where $i=1$ or $j=1$ holds, its value is one of $0$, $1$ and $2$ and given ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc107_e"},"statements":[{"statement_type":"Markdown","content":"Consider an $N \\times N$ matrix. Let us denote by $a_{i, j}$ the entry in the $i$\\-th row and $j$\\-th column. For $a_{i, j}$ where $i=1$ or $j=1$ holds, its value is one of $0$, $1$ and $2$ and given in the input. The remaining entries are defined as follows:\n\n*   $a_{i,j} = \\mathrm{mex}(a_{i-1,j}, a_{i,j-1}) (2 \\leq i, j \\leq N)$ where $\\mathrm{mex}(x, y)$ is defined by the following table:\n\n$\\mathrm{mex}(x, y)$\n\n$y=0$\n\n$y=1$\n\n$y=2$\n\n$x=0$\n\n$1$\n\n$2$\n\n$1$\n\n$x=1$\n\n$2$\n\n$0$\n\n$0$\n\n$x=2$\n\n$1$\n\n$0$\n\n$0$\n\nHow many entries of the matrix are $0, 1,$ and $2$, respectively?\n\n## Constraints\n\n*   $1 \\leq N \\leq 500{,}000$\n*   $a_{i,j}$'s given in input are one of $0$, $1$ and $2$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_{1, 1}$ $a_{1, 1}$ $...$ $a_{1, N}$\n$a_{2, 1}$\n$:$\n$a_{N, 1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc107_e","tags":[],"sample_group":[["4\n1 2 0 2\n0\n0\n0","7 4 5\n\nThe matrix is as follows:\n\n1 2 0 2\n0 1 2 0\n0 2 0 1\n0 1 2 0"]],"created_at":"2026-03-03 11:01:13"}}