Bedtime Reading I

Given an integer I, compute the sum of all its divisors.

Easy2MathNumber theoryBrute forceNo attempts yetTime limit2sMemory limit512 MB

Description

Examples3

Problem

The sigma function of a number is the sum of that number's divisors. For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12, so the sigma function of 12 is 28.

Given an integer $I$ , compute the sigma function of $I$ .

Input

The first line contains an integer $I$ ( $1 \le I \le 1\,000\,000$ ).

Output

Print the sum of all divisors of $I$ on the first line.