Define \(F(n)=\sqrt{1+\sqrt{2+\sqrt{3+\cdots+\sqrt n}}}\). Given \(n\), compute \(F(n)\).

Input

One positive integer \(n\).

The input satisfies:

• \(n >= 1\)

Output

Print the legacy labels followed by \(F(n)\) with exactly five digits after the decimal point.

Example

Input

1

Output

N = F(n) = 1.00000