github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3>Read problems statements in <a target="_blank" 
href="http://www.codechef.com/download/translated/APRIL18/mandarin/AVGPR.pdf">Mandarin chinese</a>, <a target="_blank" 
href="http://www.codechef.com/download/translated/APRIL18/russian/AVGPR.pdf">Russian</a> and <a target="_blank" 
href="http://www.codechef.com/download/translated/APRIL18/vietnamese/AVGPR.pdf">Vietnamese</a> as well.</h3>

You are given an integer sequence $A$ with length $N$.

Find the number of (unordered) pairs of elements such that the average of these two elements is also present in the sequence. Formally, find the number of pairs $(i,j)$ such that $1 \le i \lt j \le N$ and there is an index $k$ ($1 \le k \le N$) for which $2A_k = A_i+A_j$ holds.

### Input
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.

### Output
For each test case, print a single line containing one integer — the number of valid pairs $(i,j)$.

### Constraints 
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $|A_i| \le 10^3$ for each valid $i$

### Subtasks

**Subtask #1 (30 points):** $1 \le N \le 10^3$

**Subtask #2 (70 points):** $1 \le N \le 10^5$

### Example Input
<pre><tt>
3
2
2 2
3
2 1 3
6
4 2 5 1 3 5
</tt></pre>

### Example Output
<pre><tt>
1
1
7
</tt></pre>

### Explanation
**Example case 1:** We can take $k$ for $A_k$ to be either 1 or 2, since $A_k=2$ either way. Since the problem asks for unordered pairs, $(1,2)$ is the only possible valid pair (the same as $(2,1)$). Hence, the answer is 1.

**Example case 2:** We see that $A_1 = 2 = (1+3)/2$. No other valid pair exists.