Description

Given $n$, compute

where $\gcd(i, j)$ denotes the greatest common divisor of $i$ and $j$.

Input Format

The input consists of a single line with one integer, denoting $n$.

Output Format

Output a single line with one integer representing the answer.

10

67

Hint

Constraints

• For 40% of the testdata, $n \leq 2 \times 10^3$.
• For 100% of the testdata, $2 \leq n \leq 2 \times 10^6$.

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