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B. Array Reodering

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

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

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.

Example

Input

3 4 3 6 5 3 2 1 7 5 1 4 2 4 1

Output

4 0 9

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: $$$[4, 4, 2, 1, 1]$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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