You've got a cylindrical cup. Its bottom diameter and top diameter are $2$ units and its height is $2$ units as well.

The height of liquid level in the cup is $d$ ($0\le d\le 2$). When you incline the cup to the maximal angle such that the liquid inside has not been poured out, what is the area of the surface of the liquid?

Input

The first line is the number of test cases. For each test case, the first line contains a float-point number $d$.

Output

For each test case, output a line containing the area of the surface with the precision of 5 digits.

Any output with the relative or the absolute error within $10^{-5}$ will be considered correct.

Example

Input

4
0
1
2
0.424413182

Output

0.00000
4.44288
3.14159
3.51241