Bovine Dilemma

题意翻译

在一个平面直角坐标系中，有一点 $P(0,1)$。 同时在 $x$ 轴上有 $n$ 个点 $(x_1,0),(x_2,0),...,(x_n,0)$。 每次可以从 $n$ 个点中选两个点与点 $P$ 组成三角形，并记录它的面积。 问所有情况一共能组成多少种不同的面积。 **该题有 $t$ 组数据，$1 \le t \le 100$，$1 \le n,x_i \le 50$，保证 $x_i$ 严格单调递增。** 翻译提供：HoshizoraZ

题目描述

Argus was charged with guarding Io, which is not an ordinary cow. Io is quite an explorer, and she wanders off rather frequently, making Argus' life stressful. So the cowherd decided to construct an enclosed pasture for Io. There are $ n $ trees growing along the river, where Argus tends Io. For this problem, the river can be viewed as the $ OX $ axis of the Cartesian coordinate system, and the $ n $ trees as points with the $ y $ -coordinate equal $ 0 $ . There is also another tree growing in the point $ (0, 1) $ . Argus will tie a rope around three of the trees, creating a triangular pasture. Its exact shape doesn't matter to Io, but its area is crucial to her. There may be many ways for Argus to arrange the fence, but only the ones which result in different areas of the pasture are interesting for Io. Calculate the number of different areas that her pasture may have. Note that the pasture must have nonzero area.

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains an integer $ t $ ( $ 1 \leq t \leq 100 $ ) — the number of test cases. Then $ t $ test cases follow, each one is described in two lines. In the first line of each test case there is a single integer $ n $ ( $ 1 \leq n \leq 50 $ ) denoting the number of trees growing along the river. Next line contains $ n $ distinct integers $ x_1 < x_2 < \ldots < x_{n - 1} < x_n $ ( $ 1 \leq x_i \leq 50 $ ), the $ x $ -coordinates of trees growing along the river.

输出格式

In a single line output an integer, the number of different nonzero areas that triangles with trees as vertices may have.

输入输出样例

输入样例 #1

8
4
1 2 4 5
3
1 3 5
3
2 6 8
2
1 2
1
50
5
3 4 5 6 8
3
1 25 26
6
1 2 4 8 16 32

输出样例 #1

4
2
3
1
0
5
3
15

说明

In the first test case, we have $ 6 $ non-degenerate triangles with the following areas: $ 0.5 $ , $ 0.5 $ , $ 1 $ , $ 1.5 $ , $ 1.5 $ and $ 2 $ . The pasture can have $ 4 $ different areas, and thus $ 4 $ is the answer. In the second test case, we have $ 3 $ non-degenerate triangles with the following areas: $ 1 $ , $ 1 $ and $ 2 $ . The pasture can have $ 2 $ different areas, so $ 2 $ is the answer. The following two drawings present the situation in the second test case. The blue triangles in the first drawing have area $ 1 $ . The red triangle in the second drawing has area $ 2 $ .