CF1462E1.Close Tuples (easy version)

This is the easy version of this problem. The only difference between easy and hard versions is the constraints on $k$ and $m$ (in this version $k=2$ and $m=3$). Also, in this version of the problem, you DON'T NEED to output the answer by modulo.

You are given a sequence $a$ of length $n$ consisting of integers from $1$ to $n$. The sequence may contain duplicates (i.e. some elements can be equal).

Find the number of tuples of $m = 3$ elements such that the maximum number in the tuple differs from the minimum by no more than $k = 2$. Formally, you need to find the number of triples of indices $i \lt j \lt z$ such that

$$\\max(a\_i, a\_j, a\_z) - \\min(a\_i, a\_j, a\_z) \\le 2.$$

For example, if $n=4$ and $a=[1,2,4,3]$, then there are two such triples ($i=1, j=2, z=4$ and $i=2, j=3, z=4$). If $n=4$ and $a=[1,1,1,1]$, then all four possible triples are suitable.

这是本题的简单版本。简单版本与困难版本的唯一区别在于对 $k$ 和 $m$ 的约束（在本版本中 $k=2$ 且 $m=3$）。此外，在本版本中，无需将答案对某个数取模。

给定一个长度为 $n$ 的序列 $a$，其中每个元素均为 $1$ 到 $n$ 之间的整数。该序列可能包含重复元素（即某些元素可能相等）。

请找出满足以下条件的、由 $m = 3$ 个元素组成的元组的个数：元组中最大值与最小值之差不超过 $k = 2$。形式化地说，你需要找出满足如下条件的三元下标组 $(i, j, z)$（其中 $i \lt j \lt z$）的个数：

$$\max(a_i, a_j, a_z) - \min(a_i, a_j, a_z) \le 2.$$

例如，若 $n=4$ 且 $a=[1,2,4,3]$，则存在两个满足条件的三元组（对应下标为 $i=1, j=2, z=4$ 和 $i=2, j=3, z=4$）。若 $n=4$ 且 $a=[1,1,1,1]$，则所有 $\binom{4}{3}=4$ 个可能的三元组均满足条件。

The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^5$) — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains an integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the sequence $a$.

The next line contains $n$ integers $a_1, a_2,\ldots, a_n$ ($1 \le a_i \le n$) — the sequence $a$.

It is guaranteed that the sum of $n$ for all test cases does not exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^5$）—— 测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 序列 $a$ 的长度。

下一行包含 $n$ 个整数 $a_1, a_2,\ldots, a_n$（$1 \le a_i \le n$）—— 序列 $a$。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

Output $t$ answers to the given test cases. Each answer is the required number of triples of elements, such that the maximum value in the triple differs from the minimum by no more than $2$. Note that in difference to the hard version of the problem, you don't need to output the answer by modulo. You must output the exact value of the answer.

输出 $t$ 个测试用例的答案。每个答案为满足以下条件的三元组（由数组中三个元素构成）的数量：该三元组中的最大值与最小值之差不超过 $2$。注意，与本题的困难版本不同，你无需将答案对某个数取模；你必须输出答案的精确值。