The Function#1177

The Function

20 seconds
64 megabytes
Hard

Given a positive integer , compute the value of the function :

Here denotes integer division.

Since can be very large, output .

Input

The first line contains , the number of test cases. Each of the next lines contains the value of for each test case.

It is guaranteed that 1 \leq T \leq 50, 1 \leq N \leq 10^9.

Output

Output lines, where the -th line contains the answer for the -th test case.

Examples

Example 1

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