Android devices have an unlock pattern screen represented by a $3 imes$ $3$ grid of buttons numbered from $1$ through $9$.

Given two integers m and n, return the total number of unique and valid unlock patterns with a length between m and n inclusive.

A valid unlock pattern satisfies the following rules:

• Each pattern consists of a sequence of distinct buttons.

• The length of the sequence must be at least m and at most n.

• Moving between two consecutive buttons is valid if the direct line segment between them does not pass through any other button, or if every intermediate button lying directly on that line segment has already appeared earlier in the sequence.

Constraints:

• $1 \leq$ m, n $\leq 9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.