{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\le T \\le 100$\n*   $1 \\le N \\le 10^9$"},{"iden":"input","content":"The 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$N$"},{"iden":"sample input 1","content":"4\n1\n2\n5\n998244353"},{"iden":"sample output 1","content":"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: $(1,1,1),(2,1,1),(1,2,1),(1,1,2)$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}