2226 - [Spoj 5971] LCMSum

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.

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.

Examples

Input

3
1
2
5

Output

1
4
55

Hint

Constraints

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

Time Limit 1 second
Memory Limit 128 MB
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