{"problem":{"name":"Tuple of Integers","description":{"content":"You are given an integer $N$.   Find the number of non-negative integer quadruples $(a, b, c, d)$ that satisfy all of the following conditions, and output the result modulo $998244353$: *   $a + b + ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_b"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $N$.  \nFind the number of non-negative integer quadruples $(a, b, c, d)$ that satisfy all of the following conditions, and output the result modulo $998244353$:\n\n*   $a + b + c + d = N$\n*   $a$ is $0$ or $1$\n*   $b$ is $0$, $1$, or $2$\n*   $c$ is even\n*   $d$ is a multiple of $3$\n\n## Constraints\n\n*   $0 \\leq N \\leq 10^9$\n*   $N$ is an integer\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_b","tags":[],"sample_group":[["5","6\n\nThe following $6$ quadruples $(a,b,c,d)$ satisfy the conditions:\n\n*   $(0,0,2,3)$\n*   $(0,1,4,0)$\n*   $(0,2,0,3)$\n*   $(1,0,4,0)$\n*   $(1,1,0,3)$\n*   $(1,2,2,0)$"],["1000000000","1755648"]],"created_at":"2026-03-03 11:01:14"}}