{"problem":{"name":"Choosing Points","description":{"content":"Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a _good set_ when $S$ satisfies both of the following conditions: *   The dis","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc025_d"},"statements":[{"statement_type":"Markdown","content":"Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a _good set_ when $S$ satisfies both of the following conditions:\n\n*   The distance between any two points in $S$ is not $\\sqrt{D_1}$.\n*   The distance between any two points in $S$ is not $\\sqrt{D_2}$.\n\nHere, $D_1$ and $D_2$ are positive integer constants that Takahashi specified.\nLet $X$ be a set of points $(i,j)$ on a coordinate plane where $i$ and $j$ are integers and satisfy $0 ≤ i,j < 2N$.\nTakahashi has proved that, for any choice of $D_1$ and $D_2$, there exists a way to choose $N^2$ points from $X$ so that the chosen points form a good set. However, he does not know the specific way to choose such points to form a good set. Find a subset of $X$ whose size is $N^2$ that forms a good set.\n\n## Constraints\n\n*   $1 ≤ N ≤ 300$\n*   $1 ≤ D_1 ≤ 2×10^5$\n*   $1 ≤ D_2 ≤ 2×10^5$\n*   All values in the input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $D_1$ $D_2$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc025_d","tags":[],"sample_group":[["2 1 2","0 0\n0 2\n2 0\n2 2\n\nAmong these points, the distance between $2$ points is either $2$ or $2\\sqrt{2}$, thus it satisfies the condition."],["3 1 5","0 0\n0 2\n0 4\n1 1\n1 3\n1 5\n2 0\n2 2\n2 4"]],"created_at":"2026-03-03 11:01:14"}}