Given a positive number N. You need to write a program to find the maximum sum of distinct numbers such that the LCM of all these numbers is equal to N.
First line of input contains a single integer T which denotes the number of test cases. Then T test cases follows. First line of each test case contains a single integer N.
For each test case print the maximum sum of distinct numbers such that the LCM of all these numbers is equal to N.
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