Problem Statement

Find the number of pairs $(P,Q)=((P_1,P_2,\\cdots,P_N),(Q_1,Q_2,\\cdots,Q_N))$ of permutations of $(1,2,\\cdots,N)$ that satisfy the following condition, modulo $998244353$.

• For every $i$ ($1 \\leq i \\leq N-1$), one of the two conditions below holds.
  • $P_i < P_{i+1}$ and $Q_i < Q_{i+1}$.
  • $P_i > P_{i+1}$ and $Q_i > Q_{i+1}$.

Constraints

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

Input

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

$N$

Output

Print the answer.

Sample Input 1

2

Sample Output 1

2

Two pairs, $(P,Q)=((1,2),(1,2))$ and $(P,Q)=((2,1),(2,1))$, satisfy the condition.

Sample Input 2

3

Sample Output 2

10

Sample Input 3

4

Sample Output 3

88

Sample Input 4

10

Sample Output 4

286574791