B. The BOSS Can Count Pairs
brute force; math
You are given two arrays \(a\) and \(b\), both of length \(n\).Your task is to count the number of pairs of integers \((i,j)\) such that \(1 \leq i < j \leq n\) and \(a_i \cdot a_j = b_i+b_j\).
Each test contains multiple test cases. The first line of input contains a single integer \(t\) (\(1 \le t \le 10^4\)) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer \(n\) (\(2 \le n \le 2 \cdot 10^5\)) — the length of the arrays.The second line of each test case contains \(n\) integers \(a_1,a_2,\ldots,a_n\) (\(1 \le a_i \le n\)) — the elements of array \(a\).The third line of each test case contains \(n\) integers \(b_1,b_2,\ldots,b_n\) (\(1 \le b_i \le n\)) — the elements of array \(b\).It is guaranteed that the sum of \(n\) across all test cases does not exceed \(2 \cdot 10^5\).
For each test case, output the number of good pairs.
In the first sample, there are \(2\) good pairs: \((1,2)\), \((1,3)\). In the second sample, there are \(7\) good pairs: \((1,2)\), \((1,5)\), \((2,8)\), \((3,4)\), \((4,7)\), \((5,6)\), \((5,7)\).