Problem Statement

Let us consider the problem below for $a permutation P = (P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N)$, and denote the answer by f(P).

We have an $(N+2)\times (N+2)$ grid, where the rows are numbered $0, 1, \ldots, N+1$ from top to bottom and the columns are numbered $0, 1, \ldots, N+1$ from left to right. Let (i,j) denote the square at the i-th row and j-th column.
Consider paths from (0, 0) to (N+1, N+1) where we repeatedly move one square right or one square down. However, for each $1\leq i\leq N$, we must not visit the square (i, P_i). How many such paths are there?

You are given a positive integer N and an integer sequence $A = (A_1, A_2, \ldots, A_N)$, where each A_i is -1 or an integer between 1 and N (inclusive).
Consider all permutations $P = (P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N) satisfying A_i\neq -1 \implies P_i = A_i.$ Find the sum of f(P) over all such P, modulo 998244353.

Input

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

Output

Print the answer.

Constraints

• $1\leq N\leq 200$
• A_i = -1 or $1\leq A_i\leq N$.
• $A_i\neq A_j$ if $A_i\neq -1$ and $A_j\neq -1$, for $i\neq j$.

Sample Input 1

4
1 -1 4 -1

Sample Output 1

41

We want to find the sum of f(P) over two permutations P = (1,2,4,3) and P = (1,3,4,2). The figure below shows the impassable squares for each of them, where . and # represent a passable and impassable square, respectively.
...... ......
.#.... .#....
..#... ...#..
....#. ....#.
...#.. ..#...
...... ......
P=(1,2,4,3) P=(1,3,4,2)

• For P = (1,2,4,3), we have f(P) = 18.
• For P = (1,3,4,2), we have f(P) = 23.

The answer is the sum of them: 41.

Sample Input 2

4
4 3 2 1

Sample Output 2

2

In this sample, we want to compute f(P) for just one permutation P = (4,3,2,1).

Sample Input 3

3
-1 -1 -1

Sample Output 3

48

• For P = (1,2,3), we have f(P) = 10.
• For P = (1,3,2), we have f(P) = 6.
• For P = (2,1,3), we have f(P) = 6.
• For P = (2,3,1), we have f(P) = 12.
• For P = (3,1,2), we have f(P) = 12.
• For P = (3,2,1), we have f(P) = 2.

The answer is the sum of them: 48.

见题面 Input 部分

见题面 Output 部分