Let L to be an n×n square lattice, you can consider its points as (x, y), where x and y are integers from the [1, n] interval. And let f(n) to be the expected distance between two not necessarily distinct points on the lattice. For example f(1)=0 and f(2)=(2 + √ 2  ) / 4.

Input

There is no input.

Output

5000 lines, on the n-th line give the value of f(n) by 2 digits after the decimal point.

Example

Input:
No input.

Output:
0.00
0.85
1.45
2.01
2.55
.
.
.
2607.03