Problem Statement

You are given a sequence of integers $(X_1,\dots,X_M)$ of length $M$ consisting of $1,\dots,K$.

Find the number of sequences $(A_1,\dots,A_N)$ of length $N$ consisting of $1,\dots,K$ that satisfy the following condition, modulo $998244353$:

• Among all sequences of length $M$ consisting of $1,\dots,K$, the only sequence that cannot be obtained as a (not necessarily contiguous) subsequence of $(A_1,\dots,A_N)$ is $(X_1,\dots,X_M)$.

Constraints

• $2\le M,K \le N \le 400$
• $1\le X_i \le K$
• All input values are integers.

Input

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

N M K
X_1 X_2 \dots X_M

Output

Print the number of sequences satisfying the condition, modulo $998244353$.