Description: You are given an array $$$a$$$ consisting of $$$n$$$ integers. Let's call a pair of indices $$$i$$$, $$$j$$$ good if $$$1 \le i < j \le n$$$ and $$$\gcd(a_i, 2a_j) > 1$$$ (where $$$\gcd(x, y)$$$ is the greatest common divisor of $$$x$$$ and $$$y$$$). Find the maximum number of good index pairs if you can reorder the array $$$a$$$ in an arbitrary way. Input Format: The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The first line of the test case contains a single integer $$$n$$$ ($$$2 \le n \le 2000$$$) — the number of elements in the array. The second line of the test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^5$$$). It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2000$$$. Output Format: For each test case, output a single integer — the maximum number of good index pairs if you can reorder the array $$$a$$$ in an arbitrary way. Note: In the first example, the array elements can be rearranged as follows: $$$[6, 3, 5, 3]$$$. In the third example, the array elements can be rearranged as follows: $$$[4, 4, 2, 1, 1]$$$.