URI Online Judge | 2166

Square Root of 2

By M.C. Pinto, UNILA BR Brazil

Timelimit: 1

The method of periodic continued fractions is one of the many ways to calculate the square root of a natural number. This method uses as denominator a repetition for fractions. This repetition can be done by a fixed number of times.

For example, by repeating 2 times the continued fraction to calculate the square root of 2, we have the following equation.

Your task is to calculate the approximate value of square root of 2 given the number N of repetitions.

Input

The input is a natural number N (0 ≤ N ≤ 100) that indicates the quantity of denominator repetitions in the continued fraction.

Output

The output is the approximate value of the square root with 10 decimal places.

Input Samples Output Samples

0

1.0000000000

1

1.5000000000

5

1.4142857143