A14283 | Number of Pairs

You are given an array $a$ of $n$ integers. Find the number of pairs $(i, j)$ ( $1 \le i < j \le n$ ) where the sum of $a_i + a_j$ is greater than or equal to $l$ and less than or equal to $r$ (that is, $l \le a_i + a_j \le r$ ).

For example, if $n = 3$ , $a = [5, 1, 2]$ , $l = 4$ and $r = 7$ , then two pairs are suitable:

- $i=1$ and $j=2$ ( $4 \le 5 + 1 \le 7$ );
- $i=1$ and $j=3$ ( $4 \le 5 + 2 \le 7$ ).

The first line contains an integer $t$ ( $1 \le t \le 10^4$ ). Then $t$ test cases follow.

The first line of each test case contains three integers $n, l, r$ ( $1 \le n \le 2 \cdot 10^5$ , $1 \le l \le r \le 10^9$ ) — the length of the array and the limits on the sum in the pair.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ).

It is guaranteed that the sum of $n$ overall test cases does not exceed $2 \cdot 10^5$ .

For each test case, output a single integer — the number of index pairs $(i, j)$ ( $i < j$ ), such that $l \le a_i + a_j \le r$ .