Problem Statement

You are given a sequence of integers $(A_1,\dots,A_N)$ of length $N$. This sequence satisfies $0\le A_i < i$ for each $i=1,\dots,N$. Find the number of permutations $(P_1,\dots,P_N)$ of $(1,\dots,N)$ that satisfy the following conditions, modulo $998244353$.

• For each $i=1,\dots,N$:
• $P_j > P_i$ for any integer $j$ with $A_i < j < i$
  • $P_{A_i} < P_i$ if $A_i > 0$

For the sequence $(A_1,\dots,A_N)$ given in the input, it is guaranteed that there exists a permutation satisfying the conditions.

Constraints

• $1\le N\le 3\times 10^5$
• $0\le A_i \lt i$
• For $A_1,\dots,A_N$, there exists a permutation satisfying the conditions in the problem statement.
• All input values are integers.

Input

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

N
A_1 A_2 \dots A_N

Output

Print the number of permutations satisfying the conditions, modulo $998244353$.