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A. Tricky Sum

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn this problem you are to calculate the sum of all integers from 1 to *n*, but you should take all powers of two with minus in the sum.

For example, for *n* = 4 the sum is equal to - 1 - 2 + 3 - 4 = - 4, because 1, 2 and 4 are 2^{0}, 2^{1} and 2^{2} respectively.

Calculate the answer for *t* values of *n*.

Input

The first line of the input contains a single integer *t* (1 ≤ *t* ≤ 100) — the number of values of *n* to be processed.

Each of next *t* lines contains a single integer *n* (1 ≤ *n* ≤ 10^{9}).

Output

Print the requested sum for each of *t* integers *n* given in the input.

Examples

Input

2

4

1000000000

Output

-4

499999998352516354

Note

The answer for the first sample is explained in the statement.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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