{"problem":{"name":"Unbalanced Squares","description":{"content":"We have an $N \\times N$ grid. Let $(i,j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left in this grid.   Find one way to write an integer on every square to satisfy","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc142_b"},"statements":[{"statement_type":"Markdown","content":"We have an $N \\times N$ grid. Let $(i,j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left in this grid.  \nFind one way to write an integer on every square to satisfy the conditions below.\n\n*   Each integer between $1$ and $N^2$ is written exactly once.\n*   For every pair of integers $i,j\\, (1 \\leq i,j \\leq N)$, the square $(i,j)$ satisfies the following.\n    *   Among the squares horizontally, vertically, or diagonally adjacent to $(i,j)$ (there are at most eight of them), let $a$ and $b$ be the number of squares with integers larger than and smaller than that of $(i,j)$, respectively. Then, $a \\neq b$ holds.\n\nUnder the Constraints of this problem, it can be proved that such a way to write integers always exists.\n\n## Constraints\n\n*   $2 \\leq N \\leq 500$\n*   $N$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc142_b","tags":[],"sample_group":[["2","1 2\n3 4\n\nThis output contains each integer between $1$ and $N^2\\, (=4)$ exactly once, so the first condition is satisfied.  \nAdditionally, among the squares horizontally, vertically, or diagonally adjacent to the square $(1,1)$, three squares $(1,2)$, $(2,1)$, and $(2,2)$ have integers larger than that of $(1,1)$, and none has an integer smaller than that.  \nThus, for $(1,1)$, we have $a=3$ and $b=0$, so $a\\neq b$ holds.  \nSimilarly, it can be verified that $a\\neq b$ also holds for the other squares, so the second condition is satisfied.  \nTherefore, this output is valid."],["3","1 2 3\n5 4 6\n7 8 9"]],"created_at":"2026-03-03 11:01:14"}}