Problem8970--[yosupo] Number Theory - Sum of Totient Function

8970: [yosupo] Number Theory - Sum of Totient Function

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Time Limit : 2.200 sec  Memory Limit : 512 MiB

Description

Print $\sum_{i=1}^N \phi(i) \bmod 998244353$.

Input

$N$

Constraints

$1 \leq N \leq 10^{10}$

Sample 1 Input

5

Sample 1 Output

10

Sample 2 Input

6

Sample 2 Output

12

Sample 3 Input

8

Sample 3 Output

22

HINT

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