Divisor Summation

Time Limit: Java: 5000 ms / Others: 5000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

Description

Give a natural number n (1 <= n <= 500000), please tell the summation of all its proper divisors.

Definition: A proper divisor of a natural number is the divisor that is strictly less than the number.

e.g. number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22.


Input

An integer stating the number of test cases, and that many lines follow each containing one integer between 1 and 500000.


Output

One integer each line: the divisor summation of the integer given respectively.


Sample Input

3
2
10
20

Sample Output

1
8
22

Hint

None

Source

ZOJ Monthly, March 2004

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