Problem Statement

You are given a sequence of N positive integers: $A=(A_1,A_2,\dots,A_N)$.
How many integer sequences B consisting of integers between 1 and N (inclusive) satisfy all of the following conditions? Print the count modulo 998244353.

• For each integer i such that $1 \le i \le N,$ there are exactly A_i occurrences of i in B.
• For each integer i such that $1 \le i \le |B|-1$, it holds that |B_i - B_{i+1}|=1.

Input

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

Output

Print the answer.

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le A_i \le 2 \times 10^5$
• All values in input are integers.

Sample Input 1

3
2 3 1

Sample Output 1

6

B can be the following six sequences.

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

Thus, the answer is 6.

Sample Input 2

1
200000

Sample Output 2

0

There may be no sequence that satisfies the conditions.

Sample Input 3

6
12100 31602 41387 41498 31863 12250

Sample Output 3

750337372

见题面 Input 部分

见题面 Output 部分