Biswa and Universe and Randomness

Biswa has been thinking about the universe and its randomness nowadays. He dreams about some sort of objects in his sleep. These objects have a similar property. Every point on the surface of the object has similar distance from its center. If he dreams about a $N$ dimensional object, he places $N + 1$ points randomly on its surface. Now he wonders what is the probability that the shape (for 2D object the shape will be a triangle, for 3D object the shape will be a tetrahedron, and so on) created by those points will not contain the center of the object?

In the figure, there are 2 possible shape configurations for a 2D object.

Input

The first line of the test case contains a positive integer $T$ ($T ≤ 100$) denoting the number of test cases. Then in the following $T$ lines, there will be a positive integer $N$ ($2 ≤ N ≤ 100$) in each line denoting the dimension.

Output

For each case, the required probability should be given as output. Errors less than $10^{-6}$ will be ignored.

Sample

2
100
99

1.00
1.00