{"raw_statement":[{"iden":"problem statement","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 $3$"},{"iden":"constraints","content":"*   $0 \\leq N \\leq 10^9$\n*   $N$ is an integer"},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"5"},{"iden":"sample output 1","content":"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*   $(1,2,2,0)$"},{"iden":"sample input 2","content":"1000000000"},{"iden":"sample output 2","content":"1755648"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}