Problem:
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Fibonacci Number

Write a program which prints $n$-th fibonacci number for a given integer $n$. The $n$-th fibonacci number is defined by the following recursive formula:

\begin{equation*}
fib(n)= \left \{
\begin{array}{ll}
1　 & (n = 0) \\
1　 & (n = 1) \\
fib(n - 1) + fib(n - 2) & \\
\end{array}
\right.
\end{equation*}

Input

An integer $n$ is given.

output

Print the $n$-th fibonacci number in a line.

Constraints

$0 \leq n \leq 44$

Sample Input 1

3

Sample Output 1

3

Solution in Ruby (judge verdict: Wrong Answer)

def f(n)
  if n == 1
    return 1, 1
  elsif n % 2 == 0
    a, b = f(n / 2)
    return 2 * a * b - a ** 2, a ** 2 + b ** 2
  else
    a, b = f(n / 2)
    return a ** 2 + b ** 2, 2 * a * b + b ** 2
  end
end
puts f(gets.to_i)