A primitive calculator has been programmed that can perform the following three operations with the current number X:
- subtract 1 from X
- divide X by 2
- divide X by 3
Given a positive integer n, the calculator determines the minimum number of operations needed to obtain 1 starting from the number n.
Please enter a number: 25
n = 25
Number of operations = 5
Sequence of operations: [1 2 2 2 3]
Please enter a number: 394
n = 394
Number of operations = 10
Sequence of operations: [2 1 2 2 1 2 2 2 2 3]
Please enter a number: 6
n = 6
Number of operations = 2
Sequence of operations: [2 3]
Please enter a number: 9999
n = 9999
Number of operations = 16
Sequence of operations: [3 3 1 2 3 1 2 2 2 1 2 1 2 1 2 2]