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}.

Input

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

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分