Minimum Months for Rabbits to Reach N Pairs

Problem Description

A pair of rabbits, starting from the $3$rd month after birth, gives birth to one pair of rabbits every month. A baby rabbit, after it grows to the $3$rd month, also gives birth to one pair every month. Suppose no rabbit ever dies — for the pair of rabbits born in the $1$st month, at least in which month will the total number of rabbits reach $N$ pairs?

Input Format

The input gives one positive integer $N$ not exceeding $10000$ on one line.

Output Format

Output on one line the minimum number of months needed for the total number of rabbits to reach $N$.

Sample Input

30

Sample Output

9

Constraints

$1 \le N \le 10000$