## Problem Description

Gug is having fun with numbers! He starts off with an original number *X*, and can choose between the following operations:

- If
*X* is a multiple of 2, divide *X* by 2.
- If
*X* is a multiple of 3, divide it by 3.
- Subtract 1 from
*X*.

Gug repeats this until he is happy, which is when *X* becomes 0. Given a list of *N* integers that Gug starts with, determine for each integer *A*_{i}, the minimum operations it takes for Gug to be happy.

## Input

The first line of input will contain a single integer, *N*.

The second line of input will contain *N* integers, representing the array *A*_{i}.

## Output

The output should contain *N* lines with one integer each, with the integer on the *i*th line representing the number of operations it takes for Gug to be happy if he starts with *X* = *A*_{i}.

## Limits

Subtask 1 (30%): N = 1, 0 ≤ A_{i} ≤ 1000000..

Subtask 2 (31%): 1 ≤ N ≤ 10^{5}, 0 ≤ A_{i} ≤ 1000000.

Subtask 3 (39%): 1 ≤ N ≤ 10^{5}, 0 ≤ A_{i} ≤ 30000000.

Subtask 4 (0%): Sample Testcases.

## Sample Input 1

5
1 5 3 10 9

## Sample Output 1

1
4
2
4
3