{"problem":{"name":"Squares","description":{"content":"You are given an integer $N$. Find the number of pairs of integers $(x, y)$ that satisfy the following conditions, modulo $998244353$. *   $1 \\leq x,y \\leq N$.      *   $x^2-y$ is a square number. (A","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc125_b"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $N$. Find the number of pairs of integers $(x, y)$ that satisfy the following conditions, modulo $998244353$.\n\n*   $1 \\leq x,y \\leq N$.\n    \n*   $x^2-y$ is a square number. (Assume $0$ is also a square number.)\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{12}$\n*   All values in input are integers.\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":"arc125_b","tags":[],"sample_group":[["3","2\n\nWe have the following two pairs.\n\n*   $x=1,y=1$\n    \n*   $x=2,y=3$"],["10","8"],["10000000000","52583544"]],"created_at":"2026-03-03 11:01:14"}}