Background

Special for beginners, ^_^

Description

Given n, calculate the sum LCM(1,n) + LCM(2,n) + .. + LCM(n,n), where LCM(i,n) denotes the Least Common Multiple of the integers i and n.

Format

Input

The first line contains T the number of test cases. Each of the next T lines contain an integer n.

Output

Output T lines, one for each test case, containing the required sum.

Samples

3
1
2
5

1
4
55

Limitation

Constraints

1 <= T <= 300000 1 <= n <= 1000000