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 $|B_i - B_{i+1}|=1$.

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le A_i \le 2 \times 10^5$
• 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

Print the answer.