Delete Two Elements

题意翻译

有一个有 $n$ 个元素的数组 $a$ 。令 $k$ 为所有元素算术平均数。 求删掉其中两个元素后剩下元素算术平均数仍为 $k$ 的方案数。（注：先删掉第 $i$ 个，再删掉第 $j$ 个元素和先删掉第 $j$ 个元素，再删掉第 $i$ 个元素只算一种方案。） 输入格式 第一行有一个整数 $t$ $(1 < t < 10^4)$ 为测试数据数。 每个测试数据数第一行有一个整数 $n$ $( 3 < n < 2*10^5 )$。 下面 $1$ 行有 $n$ 个整数 $a_1,a_2,\dots,a_n$ $(0<a_1,a_2,\dots,a_n<10^9)$，其中 $a_i$ 为 $a$ 中第 $i$ 个元素。 所有 $n$ 的和 $< 2*10^5$。 输出格式 对于每个测试数据，输出一个整数表示求删掉数组 $a$ 中两个元素后剩下元素算术平均数仍为 $k$ 的方案数。

题目描述

Monocarp has got an array $ a $ consisting of $ n $ integers. Let's denote $ k $ as the mathematic mean of these elements (note that it's possible that $ k $ is not an integer). The mathematic mean of an array of $ n $ elements is the sum of elements divided by the number of these elements (i. e. sum divided by $ n $ ). Monocarp wants to delete exactly two elements from $ a $ so that the mathematic mean of the remaining $ (n - 2) $ elements is still equal to $ k $ . Your task is to calculate the number of pairs of positions $ [i, j] $ ( $ i < j $ ) such that if the elements on these positions are deleted, the mathematic mean of $ (n - 2) $ remaining elements is equal to $ k $ (that is, it is equal to the mathematic mean of $ n $ elements of the original array $ a $ ).

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of testcases. The first line of each testcase contains one integer $ n $ ( $ 3 \le n \le 2 \cdot 10^5 $ ) — the number of elements in the array. The second line contains a sequence of integers $ a_1, a_2, \dots, a_n $ ( $ 0 \le a_i \le 10^{9} $ ), where $ a_i $ is the $ i $ -th element of the array. The sum of $ n $ over all testcases doesn't exceed $ 2 \cdot 10^5 $ .

输出格式

Print one integer — the number of pairs of positions $ [i, j] $ ( $ i < j $ ) such that if the elements on these positions are deleted, the mathematic mean of $ (n - 2) $ remaining elements is equal to $ k $ (that is, it is equal to the mathematic mean of $ n $ elements of the original array $ a $ ).

输入输出样例

输入样例 #1

4
4
8 8 8 8
3
50 20 10
5
1 4 7 3 5
7
1 2 3 4 5 6 7

输出样例 #1

6
0
2
3

说明

In the first example, any pair of elements can be removed since all of them are equal. In the second example, there is no way to delete two elements so the mathematic mean doesn't change. In the third example, it is possible to delete the elements on positions $ 1 $ and $ 3 $ , or the elements on positions $ 4 $ and $ 5 $ .