Longge is good at mathematics, and he likes to think about hard mathematical problems which will be solved by some graceful algorithms. Now a problem comes:
Given an integer n. Compute ∑gcd(i,n) for all 1≤i≤n.
"Oh, I know, I know!" Longge shouts! But do you know? Please solve it.
Each line contains one number n (1<n<231).
For each number n print in a separate line the sum ∑gcd(i,n) for all 1≤i≤n.