C. Number of Pairstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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). InputThe 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.OutputFor 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.ExampleInput
4
3 4 7
5 1 2
5 5 8
5 1 2 4 3
4 100 1000
1 1 1 1
5 9 13
2 5 5 1 1
Output
2
7
0
1

4
3 4 7
5 1 2
5 5 8
5 1 2 4 3
4 100 1000
1 1 1 1
5 9 13
2 5 5 1 1

2 7 0 1 
['binary search', 'data structures', 'math', 'two pointers', '*1300']