Collatz's Problem

For a positive integer n

• If n is even, divide by 2.
• If n is odd, multiply by 3 and add 1.

If you repeat the above operation, the result will be 1. A problem called "Colatz conjecture" is that repeating this operation for any positive integer n will always result in 1. This problem is an unsolved problem, also known as the "Kakutani problem" in Japan. It is known that there is no counterexample for a very large number 3 × 253 = 27,021,597,764,222,976 using a computer, but it has not been mathematically proven.

Create a program that takes the integer n as an input and outputs the number of operations that are repeated until the result is 1. The integer n should be an integer that is 1 or more and the value in the middle of repeating the above calculation is 1000000 or less. For example, if you receive 3 as input, the operation column will be

3 → 10 → 5 → 16 → 8 → 4 → 2 → 1

Therefore, 7 is output, which is the number of operations (the number of arrows above).

Input

A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n (n ≤ 1000000) is given on one row for each dataset.

The number of datasets does not exceed 50.

Output

Outputs the number of operations for each dataset on one line.

Example

Input

3 10 0

Output

7 6

inputFormat

input and

outputFormat

outputs the number of operations that are repeated until the result is 1. The integer n should be an integer that is 1 or more and the value in the middle of repeating the above calculation is 1000000 or less. For example, if you receive 3 as input, the operation column will be

3 → 10 → 5 → 16 → 8 → 4 → 2 → 1

Therefore, 7 is output, which is the number of operations (the number of arrows above).

Input

A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n (n ≤ 1000000) is given on one row for each dataset.

The number of datasets does not exceed 50.

Output

Outputs the number of operations for each dataset on one line.

Example

Input

3 10 0

Output

7 6

样例

3
10
0

7
6

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