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Contest: Task: Related: TaskF TaskH

Score : $600$ points

Problem Statement

Given is a prime number $P$.

How many pairs of integers $(x, y)$ satisfy the following conditions?

  • $0 \leq x \leq P-1$
  • $0 \leq y \leq P-1$
  • There exists a positive integer $n$ such that $x^n \equiv y \pmod{P}$.

Since the answer may be enormous, print it modulo $998244353$.

Constraints

  • $2 \leq P \leq 10^{12}$
  • $P$ is a prime number.

Input

Input is given from Standard Input in the following format:

$P$

Output

Print the answer modulo $998244353$.

Sample Input 1

3

Sample Output 1

4

Four pairs $(x, y) = (0, 0), (1, 1), (2, 1), (2, 2)$ satisfy the conditions.

Sample Input 2

11

Sample Output 2

64

Sample Input 3

998244353

Sample Output 3

329133417