Description

There is a sequence of fractions $\frac{q_1}{p_1}$, $\frac{q_2}{p_2}$, $\frac{q_3}{p_3}$, $\frac{q_4}{p_4}$, $\frac{q_5}{p_5}$, ..., where $q_{i+1}=q_i+p_i$, $p_{i+1}=q_i$, $p_1=1$, and $q_1=2$. For example, the first 5 terms of this sequence are $\frac{2}{1}$, $\frac{3}{2}$, $\frac{5}{3}$, $\frac{8}{5}$, $\frac{13}{8}$. Calculate the sum of the first n terms of this sequence.

Input Format

Input consists of a single line containing a positive integer n (n≤30).

Output Format

Output consists of a single line containing a floating-point number representing the sum of the first n terms of the sequence, rounded to 4 decimal places.

Sample

2

3.5000