You are given a $0$ indexed integer array nums.

A pair of indices (i, j) is considered beautiful if $0 \leq i < j <$ nums.length and the first digit of nums[i] and the last digit of nums[j] are coprime.

Return the total number of beautiful pairs in nums.

Note: Two integers $x$ and $y$ are coprime if $\gcd(x, y) = 1$, where $\gcd(x, y)$ denotes the greatest common divisor of $x$ and $y$.

Constraints:

• $2 \leq$ nums.length $\leq 100$

• $1 \leq$ nums[i] $\leq 9999$

• nums[i] % 10 $\neq 0$

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.