Problem Statement

You are given a positive integer $N$. Print the number, modulo $998244353$, of sequences $A$ of length $3N$ that contain each integer from $1$ through $N$ three times and satisfy the following condition.

• $A$ has no contiguous subsequence of length $N$ that is a permutation of the sequence $(1, 2, \ldots, N)$.

Constraints

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

Input

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

N

Output

Print the answer.