A16123. Sum and Product

You have an array $a$ of length $n$ .

Your task is to answer $q$ queries: given $x,y$ , find the number of pairs $i$ and $j$ ( $1 \le i < j \le n$ ) that both $a_i + a_j = x$ and $a_i \cdot a_j = y$ .

That is, for the array $[1,3,2]$ and asking for $x=3,y=2$ the answer is $1$ :

- $i=1$ and $j=2$ fail because $1 + 3 = 4$ and not $3,$ also $1 \cdot 3=3$ and not $2$ ;
- $i=1$ and $j=3$ satisfies both conditions;
- $i=2$ and $j=3$ fail because $3 + 2 = 5$ and not $3,$ also $3 \cdot 2=6$ and not $2$ ;

The first line contains one integer $t$ ( $1\le t\le 10^4$ ) — the number of test cases.

The second line of each test case contains one integer $n$ ( $1 \le n \le 2\cdot 10^5$ ) — the length of the array $a$ .

The third line of each test case contains $n$ integers $a_1,a_2,\dots,a_n$ ( $1 \le |a_i| \le 10^9$ ) — array $a$ .

The fourth line of each test case contains the integer $q$ ( $1 \le q \le 2\cdot 10^5$ ) — the number of requests.

The next $q$ lines contain two numbers each $x$ and $y$ ( $1 \le |x|\le 2\cdot 10^9,1\le |y|\le 10^{18}$ ) — request.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ . This is also guaranteed for the sum of $q$ values.

For each test case print a line with $q$ numbers — the answers to the queries.

For the first test case, let's analyze each pair of numbers separately:

- pair $(a_1,a_2)$ : $a_1 + a_2 = 4$ , $a_1 \cdot a_2 = 3$
- pair $(a_1,a_3)$ : $a_1 + a_3 = 3$ , $a_1 \cdot a_3 = 2$
- pair $(a_2,a_3)$ : $a_2 + a_3 = 5$ , $a_2 \cdot a_3 = 6$

From this, we can see that for the first query, the pair $(a_1,a_3)$ is suitable, for the second query, it is $(a_2,a_3)$ , and there are no suitable pairs for the third and fourth queries.In the second test case, all combinations of pairs are suitable.