URI Online Judge | 2166
# Square Root of 2

**Timelimit: 1**

By M.C. Pinto, UNILA Brazil

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.

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

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 |