{"raw_statement":[{"iden":"problem statement","content":"The score of a permutation $P=(P_1,P_2,\\ldots,P_{2N})$ of $(1,2,\\ldots,2N)$ is defined as follows:\n\n> Consider dividing $P$ into two (not necessarily contiguous) subsequences $A = (A_1,A_2,\\ldots,A_N)$ and $B = (B_1,B_2,\\ldots,B_N)$. The score of $P$ is the maximum possible value of $\\displaystyle\\sum_{i=1}^{N}A_i B_i$ in such a division.\n\nLet $M$ be the maximum among the scores of all permutations of $(1,2,\\ldots,2N)$. Find the number, modulo $998244353$, of permutations of $(1,2,\\ldots,2N)$ with the score of $M$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2\\times 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"2"},{"iden":"sample output 1","content":"16\n\nThe maximum among the scores of the $24$ possible permutations, $M$, is $14$, and there are $16$ permutations with the score of $14$.\nFor instance, the permutation $(1,2,3,4)$ achieves $\\sum _{i=1}^{N}A_i B_i = 14$ in the division $A=(1,3), B=(2,4)$."},{"iden":"sample input 2","content":"10000"},{"iden":"sample output 2","content":"391163238\n\nPrint the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}