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Background

The Collatz Conjecture states that:

For any positive integer $x$:

• If it's odd, multiply it by $3$ and add $1$, i.e.: $x \rarr x \times 3 + 1$;

• If it's even, divide it by $2$, i.e.: $x \rarr \dfrac{x}{2}$.

By repeating these operations, the number will eventually reach $1$ and fall into the $1 \rarr 4 \rarr 2 \rarr 1 \rarr 4 \rarr \cdots$ loop.

Description

Now, write a program to calculate how many operations are needed for a positive integer $x$ to transform into $1$.

Input

A single line containing the positive integer $x$ to be processed.

Output

A non-negative integer $s$, representing the number of operations required.

7

16

8

3

Hint

【Data Scale and Convention】

For $100\%$ of the data, $1 \leq x \leq 2 \times 10^6$.