Problem Statement

The score of a permutation $P=(P_1,P_2,\ldots,P_{2N})$ of $(1,2,\ldots,2N)$ is defined as follows:

Consider dividing

P

into two (not necessarily contiguous) subsequences

A = (A_1,A_2,\ldots,A_N)

and

B = (B_1,B_2,\ldots,B_N)

. The score of

P

is the maximum possible value of

\displaystyle\sum_{i=1}^{N}A_i B_i

in such a division.

Let $M$ be the maximum among the scores of all permutations of $(1,2,\ldots,2N)$. Find the number, modulo $998244353$, of permutations of $(1,2,\ldots,2N)$ with the score of $M$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.