Collatz Problem

A sequence a=\{a_1,a_2,a_3,......\} is determined as follows:

• The first term s is given as input.

• Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.

• a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.

Find the minimum integer m that satisfies the following condition:

• There exists an integer n such that a_m = a_n (m > n).

Constraints

• 1 \leq s \leq 100
• All values in input are integers.
• It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum integer m that satisfies the condition.

Examples

Input

8

Output

5

Input

7

Output

18

Input

54

Output

114

inputFormat

input.

• Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.

• a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.

Find the minimum integer m that satisfies the following condition:

• There exists an integer n such that a_m = a_n (m > n).

Constraints

• 1 \leq s \leq 100
• All values in input are integers.
• It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.

Input

Input is given from Standard Input in the following format:

s

outputFormat

Output

Print the minimum integer m that satisfies the condition.

Examples

Input

8

Output

5

Input

7

Output

18

Input

54

Output

114

样例

54

114