{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 ≤ N ≤ 300$\n*   $1 ≤ D_1 ≤ 2×10^5$\n*   $1 ≤ D_2 ≤ 2×10^5$\n*   All values in the input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $D_1$ $D_2$"},{"iden":"sample input 1","content":"2 1 2"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"3 1 5"},{"iden":"sample output 2","content":"0 0\n0 2\n0 4\n1 1\n1 3\n1 5\n2 0\n2 2\n2 4"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}