Problem Statement

For an integer sequence $X=(X_1,X_2,\dots,X_N)$ of length $N$ whose elements are all between $1$ and $N$ (inclusive), consider the question below, and let $f(X)$ be the answer.

There is an undirected graph

G

with

N

vertices (and possibly multi-edges and self-loops).

G

has

N

edges, the

i

-th of which connects Vertex

i

and Vertex

X_i

. Find the number of connected components in

G

.

You are given an integer sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$, where each $A_i$ is an integer between $1$ and $N$ (inclusive) or $-1$.

Consider an integer sequence $X=(X_1,X_2,\dots,X_N)$ of length $N$ whose elements are all between $1$ and $N$ such that $A_i \neq -1 \Rightarrow A_i = X_i$. Find the sum of $f(X)$ over all such $X$, modulo $998244353$.

Constraints

• $1 \le N \le 2000$
• $A_i$ is between $1$ and $N$ (inclusive) or $-1$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Prin the answer.