{"problem":{"name":"Triple Pair","description":{"content":"You are given a positive integer $N$. Find the number, modulo $998244353$, of triples of positive integers $(x,y,z)$ that satisfy the following condition. *   All of $xy$, $yz$, $zx$ are less than or","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc160_b"},"statements":[{"statement_type":"Markdown","content":"You are given a positive integer $N$.\nFind the number, modulo $998244353$, of triples of positive integers $(x,y,z)$ that satisfy the following condition.\n\n*   All of $xy$, $yz$, $zx$ are less than or equal to $N$.\n\nYou have $T$ test cases to solve.\n\n## Constraints\n\n*   $1 \\le T \\le 100$\n*   $1 \\le N \\le 10^9$\n\n## Input\n\nThe input is given from Standard Input in the following format, where $\\mathrm{case}_i$ represents the $i$\\-th test case:\n\n$T$\n$\\mathrm{case}_1$\n$\\mathrm{case}_2$\n$\\vdots$\n$\\mathrm{case}_T$\n\nEach test case is in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc160_b","tags":[],"sample_group":[["4\n1\n2\n5\n998244353","1\n4\n17\n727512986\n\nIn the first test case, $N=1$. There is one triple $(x,y,z)$ that satisfies the condition: $(1,1,1)$.\nIn the second test case, $N=2$. There are four triples $(x,y,z)$ that satisfy the condition: $(1,1,1),(2,1,1),(1,2,1),(1,1,2)$."]],"created_at":"2026-03-03 11:01:14"}}