B. a math problem
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

This is an easy math problem.

We define a function $$$f(x)$$$ to represent how many pairs of factors $$$(p,q)$$$ of $$$x$$$ satisfy that $$$p$$$ and $$$q$$$ are coprime. When $$$p\not=q$$$ , $$$(p,q)$$$ and $$$(q,p)$$$ are different pairs.

$$$$$$ f(x)=\sum_{p,q|x}[ gcd(p,q)=1 ] $$$$$$

Now we want to calculate

$$$$$$ g(n)=\sum_{i=1}^n f(i) $$$$$$

The answer maybe too large, so you only need to output the result of its modulo of 998244353

Input

A single integer $$$n(1\le n\le 10^{10})$$$

Output

A single integer $$$g(n)$$$

Example
Input
10
Output
48