598_A. Tricky Sum
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 20, 21 and 22 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 ≤ 109).

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.
```python
t = int(input())

while(t):
    
    n = int(input())
    
    s = n*(n+1) // 2
    
    k = len(format(n, "b"))
    
    s_pair = 2**k - 1
    
    print(s - 2*s_pair)
    
    t-=1
```