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

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

For each test case, output one integer — the number of interesting pairs of integers for the given sequence $a$.

见题面 Input 部分

见题面 Output 部分

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

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