Solve the programming task below in a Python markdown code block.
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You are given an integer sequence $A$ with length $N$. Find the number of ordered pairs of positive integers $(a, b)$ such that $a$ occurs in $A$ at least $b$ times and $b$ occurs in $A$ at least $a$ times. 

------  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 pairs.

------  Constraints  ------
$1 ≤ T ≤ 1,000$
$2 ≤ N ≤ 10^{6}$
$1 ≤ A_{i} ≤ 10^{6}$ for each valid $i$
the sum of $N$ over all test cases does not exceed $3 \cdot 10^{6}$

------  Subtasks ------
Subtask #1 (30 points):
$1 ≤ N ≤ 10^{5}$
the sum of $N$ over all test cases does not exceed $3 \cdot 10^{5}$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------ 
3

5

1 2 3 4 5

5

1 1 2 2 3

5

3 3 2 2 2
----- Sample Output 1 ------ 
1

4

3