SPOJ Problem Set (classical) 1754. Divisor Summation (Hard) Problem code: DIVSUM2

Given a natural number n (1 <= n <= 1e16), please output 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 (equal to 500), and that many lines follow, each containing one integer between 1 and 1e16 inclusive.

Output

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

Example

Input:
3
2
10
20

Output:
1
8
22

warning: a naive algorithm may not run in time.

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Added by:	Jin Bin
Date:	2007-08-29
Time limit:	60s
Source limit:	50000B
Languages:	All except: C99 strict ERL TECS JS
Resource:	own problem