【Codeforces】[598A]Tricky Sum

Description

In 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.