Interesting Pairs

Given an array $A$ having $N$ elements, Chef wonders how many pairs $(i, j)$ exists such that $1 \leq i \lt j \leq N$, and $A_i \cdot A_j$ is divisible by $i \cdot j$. Can you help Chef in finding the number of such pairs? ### Input - The first line of input contains a single integer $T$, denoting the number of test cases. The description of the $T$ testcases follows. - The first line of each t