{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence $A = (A_1,\\ldots,A_N)$ of length $N$. Each element of $A$ is either $-1$ or an integer between $1$ and $N$, and each integer from $1$ to $N$ is contained at most once.\nA permutation $P=(P_1,\\ldots,P_N)$ of $(1,\\ldots,N)$ is called a **good permutation** if and only if it satisfies $A_i \\neq -1 \\Rightarrow P_i = A_i$. Find the sum of the squares of the inversion numbers of all good permutations, modulo $998244353$.\nThe inversion number of a permutation $P$ is the number of pairs of integers $(i,j)$ such that $1\\leq i < j \\leq N$ and $P_i > P_j$."},{"iden":"constraints","content":"*   $1\\leq N\\leq 3000$\n*   $A_i = -1$ or $1\\leq A_i \\leq N$.\n*   Each integer from $1$ to $N$ is contained at most once in $A$.\n*   All input values are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ \n$A_1$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"4\n3 -1 2 -1"},{"iden":"sample output 1","content":"29\n\nThere are two good permutations: $P=(3,1,2,4)$ and $P=(3,4,2,1)$, with inversion numbers $2$ and $5$, respectively.\nThus, the answer is $2^2 + 5^2 = 29$."},{"iden":"sample input 2","content":"10\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1"},{"iden":"sample output 2","content":"952235647"},{"iden":"sample input 3","content":"15\n-1 -1 10 -1 -1 -1 2 -1 -1 3 -1 -1 -1 -1 1"},{"iden":"sample output 3","content":"460544744\n\nFind the sum modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}