Stickogon
Description
You are given $n$ sticks of lengths $a_1, a_2, \ldots, a_n$. Find the maximum number of regular (equal-sided) polygons you can construct simultaneously, such that:
- Each side of a polygon is formed by exactly one stick.
- No stick is used in more than $1$ polygon.
Note: Sticks cannot be broken.
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \leq n \leq 100$) — the number of sticks available.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 100$) — the stick lengths.
For each test case, output a single integer on a new line — the maximum number of regular (equal-sided) polygons you can make simultaneously from the sticks available.
Input
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \leq n \leq 100$) — the number of sticks available.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 100$) — the stick lengths.
Output
For each test case, output a single integer on a new line — the maximum number of regular (equal-sided) polygons you can make simultaneously from the sticks available.
4
1
1
2
1 1
6
2 2 3 3 3 3
9
4 2 2 2 2 4 2 4 4
0
0
1
2
Note
In the first test case, we only have one stick, hence we can't form any polygon.
In the second test case, the two sticks aren't enough to form a polygon either.
In the third test case, we can use the $4$ sticks of length $3$ to create a square.
In the fourth test case, we can make a pentagon with side length $2$, and a square of side length $4$.