Background

Special for beginners, ^_^

Description

Given an integer n, print the sum.

$\sum\limits_{i=1}^n \sum\limits_{j=1}^n\left(\lfloor \frac n{max(i,j)}\rfloor\cdot [ \gcd(i, j)=1] \right) mod (1234657890)$

Format

Input

每行1个$n(\le10^{19})$，不超过10万行。.

Output

每行输出一个和，

Samples

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2

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4

Limitation

1s, 1024KiB for each test case.