Remainders sum

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, 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 ≤ n ≤ 10^9).

Output

Output the sum of remainders.

Examples