The Collatz Sequence

The Collatz sequence is as follows:

• Start with some given integer n.
• If it is even, the next number will be n divided by 2.
• If it is odd, multiply it by 3 and add 1 to make the next number.
• The sequence stops when it reaches 1.

According to the Collatz conjecture, it will always reach 1. If that's true, you can construct a finite sequence following the aforementioned method for any given integer.

Write a function that takes in an integer n and returns the highest integer in the corresponding Collatz sequence.

Examples

max_collatz(10) ➞ 16
# Collatz sequence: 10, 5, 16, 8, 4, 2, 1

max_collatz(32) ➞ 32
# Collatz sequence: 32, 16, 8, 4, 2, 1

max_collatz(85) ➞ 256
# Collatz sequence: 85, 256, 128, 64, 32, 16, 8, 4, 2, 1

Notes

N/A