You are given an $m imes n$ integer matrix mat.

Select exactly one integer from each row of mat. Return the total number of ways to choose these integers such that the greatest common divisor of all the selected integers is equal to $1$.

Two choices are considered different if they select an element from a different column in at least one row.

Constraints:

• $1 \leq$ m $==$ mat.length $\leq 150$

• $1 \leq$ n $==$ mat[i].length $\leq 150$

• $1 \leq$ mat[i][j] $\leq 150$

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.