Limits 1s, 512 MB

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 NN dimensional object, he places N+1N + 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 TT (T100T ≤ 100) denoting the number of test cases. Then in the following TT lines, there will be a positive integer NN (2N1002 ≤ N ≤ 100) in each line denoting the dimension.

Output

For each case, the required probability should be given as output. Errors less than 10610^{-6} will be ignored.

Sample

InputOutput
2
100
99
1.00
1.00

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Statistics

72% Solution Ratio
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