6226:

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.

输入格式

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

输出格式

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

样例输入

3
1
2
5

样例输出

1
4
55

提示

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

题目来源

没有写明来源