Evenly Spaced Triples

There are $N$ distinct points marked on a line. Point $i$ sits at position $X_i$.

Pick three of the $N$ points and call the leftmost one $a$, the middle one $b$, and the rightmost one $c$, at positions $X_a$, $X_b$, and $X_c$. The three points are evenly spaced when the distance between $a$ and $b$ equals the distance between $b$ and $c$, that is, when $X_b - X_a = X_c - X_b$.

Here is an example with $N = 5$.

The points sit at -4, -1, 0, 2, and 4. Taking -4, -1, 0 as $a$, $b$, $c$ gives $X_b - X_a = 3$ and $X_c - X_b = 1$, so the spacing is not equal. Taking -4, -1, 2 gives $X_b - X_a = 3$ and $X_c - X_b = 3$, so those three points are evenly spaced. In this example the evenly spaced triples are (-4, -1, 2), (-4, 0, 4), and (0, 2, 4), so there are 3 of them.

Given the positions of the $N$ points, write a program that counts how many evenly spaced triples there are.

The first line contains $T$, the number of test cases. The $T$ test cases follow.

The first line of each test case contains the number of points $N$ ($3 \le N \le 1000$). The second line contains the $N$ positions $X_1, X_2, \dots, X_N$ separated by spaces. Every position is an integer between -100,000,000 and 100,000,000, and all positions are distinct.

For each test case, print the number of evenly spaced triples $a$, $b$, $c$ on its own line, in the order the test cases are given.