Problem Statement

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.

A 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 $998244353$.

The inversion number of a permutation $P$ is the number of pairs of integers $(i,j)$ such that $1\leq i < j \leq N$ and $P_i > P_j$.

Constraints

• $1\leq N\leq 3000$
• $A_i = -1$ or $1\leq A_i \leq N$.
• Each integer from $1$ to $N$ is contained at most once in $A$.
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

Print the answer.