{"raw_statement":[{"iden":"problem statement","content":"We have an $N×N$ checkerboard.\nFrom the square at the upper left corner, a square that is $i$ squares to the right and $j$ squares below is denoted as $(i, j)$. Particularly, the square at the upper left corner is denoted as $(0, 0)$.\nEach square $(i, j)$ such that $i+j$ is even, is colored black, and the other squares are colored white.\nWe will satisfy the following condition by painting some of the white squares:\n\n*   Any black square can be reached from square $(0, 0)$ by repeatedly moving to a black square that shares a side with the current square.\n\nAchieve the objective by painting at most $170000$ squares black."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 1,000$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"2"},{"iden":"sample output 1","content":"1\n1 0"},{"iden":"sample input 2","content":"4"},{"iden":"sample output 2","content":"3\n0 1\n2 1\n2 3"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}