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 Ai, 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 Ai.
Output
The output should contain N lines with one integer each, with the integer on the ith line representing the number of operations it takes for Gug to be happy if he starts with X = Ai.
Limits
Subtask 1 (30%): N = 1, 0 ≤ Ai ≤ 1000000..
Subtask 2 (31%): 1 ≤ N ≤ 105, 0 ≤ Ai ≤ 1000000.
Subtask 3 (39%): 1 ≤ N ≤ 105, 0 ≤ Ai ≤ 30000000.
Subtask 4 (0%): Sample Testcases.
Sample Input 1
5
1 5 3 10 9
Sample Output 1
1
4
2
4
3