Remainders sum#3764

Remainders sum

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Hard

Today at school Petya learnt what is the remainder and how to find it. To practice a bit, he took some integer $n$ and calculated the sum of all remainders after dividing it by all integers from $1$ to $n$ . For example, for $n = 6$ n = 6, remainders will be $0$ , $0$ , $0$ , $2$ , $1$ , and $0$ , so their sum is $3$ . Now to check his calculations he asks you to write a program to calculate this sum for any $n$ .

Input

The only line of input contains integer $n$ ( $1 \leq n \leq 1 0^{9}$ 1 \le n \le 10^9).

Output

Output the sum of remainders.

Examples

Example 1

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n = 6

1 \leq n \leq 1 0^{9}