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.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \dots A_N$

Output

Prin the answer.

Constraints

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

Sample Input 1

3
-1 1 3

Sample Output 1

5

There are three sequences X satisfying the requirement, as follows.

• X=(1,1,3), for which the answer to the question is 2.
• X=(2,1,3), for which the answer to the question is 2.
• X=(3,1,3), for which the answer to the question is 1.

Thus, the answer is 2+2+1=5.

Sample Input 2

1
1

Sample Output 2

1

Sample Input 3

8
-1 3 -1 -1 8 -1 -1 -1

Sample Output 3

433760

见题面 Input 部分

见题面 Output 部分