Briefcase Lock

A briefcase has a 4-digit rolling-lock. Each digit is a number from 0-9 that can be rolled either forwards or backwards.

Create a function that returns the smallest number of turns it takes to transform the lock from the current combination to the target combination. One turn is equivalent to rolling a number forwards or backwards by one.

To illustrate:

• current-lock: 4089
• target-lock: 5672

What is the minimum number of turns it takes to transform 4089 to 5672?

4 ➞ 5
4 ➞ 5  # Forward Turns: 1 <- Min
4 ➞ 3 ➞ 2 ➞ 1 ➞ 0 ➞ 9 ➞ 8 ➞ 7 ➞ 6 ➞ 5  # Backward Turns: 9

0 ➞ 6
0 ➞ 1 ➞ 2 ➞ 3 ➞ 4 ➞ 5 ➞ 6  # Forward Turns: 6
0 ➞ 9 ➞ 8 ➞ 7 ➞ 6  # Backward Turns: 4  <- Min

8 ➞ 7
8 ➞ 9 ➞ 0 ➞ 1 ➞ 2 ➞ 3 ➞ 4 ➞ 5 ➞ 6 ➞ 7  # Forward Turns: 9
8 ➞ 7  # Backward Turns: 1  <- Min

9 ➞ 2
9 ➞ 0 ➞ 1 ➞ 2  # Forward Turns: 3  <- Min
9 ➞ 8 ➞ 7 ➞ 6 ➞ 5 ➞ 4 ➞ 3 ➞ 2  # Backward Turns: 7

It takes 1 + 4 + 1 + 3 = 9 minimum turns to change the lock from 4089 to 5672.

Examples

min_turns("4089", "5672") ➞ 9

min_turns("1111", "1100") ➞ 2

min_turns("2391", "4984") ➞ 10

Notes

• Both locks are in string format.
• A 9 rolls forward to 0, and a 0 rolls backwards to a 9.