Problem Statement

You are given a sequence of length $N$ consisting of integers from $1$ to $N$, $A=(A_1,A_2,\\ldots,A_N)$.

Find the number, modulo $998244353$, of sequences of length $N$ consisting of integers from $1$ to $N$, $B=(B_1,B_2,\\ldots,B_N)$, that satisfy the following conditions for all $i=1,2,\\ldots,N$.

• The number of occurrences of $i$ in $B$ is at most $A_i$.
• The number of occurrences of $B_i$ in $B$ is at most $A_i$.

Constraints

• $1 \\leq N \\leq 500$
• $1 \\leq A_i \\leq N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $A_1$ $A_2$ $\\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

10

The following $10$ sequences satisfy the conditions:

• $(1,2,2)$
• $(1,2,3)$
• $(1,3,2)$
• $(1,3,3)$
• $(2,1,3)$
• $(2,3,1)$
• $(2,3,3)$
• $(3,1,2)$
• $(3,2,1)$
• $(3,2,2)$

Sample Input 2

4
4 4 4 4

Sample Output 2

256

All sequences of length $4$ consisting of integers from $1$ to $4$ satisfy the conditions, and there are $4^4=256$ such sequences.

Sample Input 3

5
1 1 1 1 1

Sample Output 3

120

All permutations of $(1,2,3,4,5)$ satisfy the conditions, and there are $5!=120$ such sequences.

Sample Input 4

14
6 5 14 3 6 7 3 11 11 2 3 7 8 10

Sample Output 4

628377683

Be sure to print the number modulo $998244353$.