Upon a table there are two boxes. Each box has N matches inside. We want to know what is the probability of choose N times a random box and take one match from it, at the end have an empty box.

You have to print all digits.

Constraints
1 ≤ T ≤ 1000
1 ≤ N ≤ 1000

Input

T
N1
N2
...
NT

Output

P1
P2
...
PT

Example

Input:
1
2

Output:
0.5