You are given a sequence $$$a$$$, consisting of $$$n$$$ integers, where the $$$i$$$-th element of the sequence is equal to $$$a_i$$$. You are also given two integers $$$x$$$ and $$$y$$$ ($$$x \le y$$$).

A pair of integers $$$(i, j)$$$ is considered interesting if the following conditions are met:

- $$$1 \le i < j \le n$$$;
- if you simultaneously remove the elements at positions $$$i$$$ and $$$j$$$ from the sequence $$$a$$$, the sum of the remaining elements is at least $$$x$$$ and at most $$$y$$$.

Your task is to determine the number of interesting pairs of integers for the given sequence $$$a$$$.

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

Each test case consists of two lines:

- The first line contains three integers $$$n, x, y$$$ ($$$3 \le n \le 2 \cdot 10^5$$$, $$$1 \le x \le y \le 2 \cdot 10^{14}$$$);
- The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^{9}$$$).

Additional constraint on the input: the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output one integer — the number of interesting pairs of integers for the given sequence $$$a$$$.
Example Input 0:
7
4 8 10
4 6 3 6
6 22 27
4 9 6 3 4 5
3 8 10
3 2 1
3 1 1
2 3 4
3 3 6
3 2 1
4 4 12
3 3 2 1
6 8 8
1 1 2 2 2 3

Example Output 0:
4
7
0
0
1
5
6

Notes:
In the first example, there are $$$4$$$ interesting pairs of integers:

1. $$$(1, 2)$$$;
2. $$$(1, 4)$$$;
3. $$$(2, 3)$$$;
4. $$$(3, 4)$$$.

Example input:
7
4 8 10
4 6 3 6
6 22 27
4 9 6 3 4 5
3 8 10
3 2 1
3 1 1
2 3 4
3 3 6
3 2 1
4 4 12
3 3 2 1
6 8 8
1 1 2 2 2 3


Example output:
4
7
0
0
1
5
6