F. Three Cuts
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of $$$n$$$ integers, where $$$n$$$ is even. You can perform the following operation until the array becomes empty:

Choose indices $$$i$$$,$$$j$$$ such that $$$i \ne j$$$, add $$$\lceil (a_i + a_j)/3 \rceil$$$ to your score, and remove $$$a_i$$$ and $$$a_j$$$ from the array.

Find the maximum score you can obtain.

Here, $$$\lceil x \rceil$$$ (the ceiling of $$$x$$$) is the smallest integer greater than or equal to $$$x$$$. For example, $$$\lceil 2.1 \rceil = 3$$$, $$$\lceil 5 \rceil = 5$$$.

Input

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 10^4)$$$ — the number of test cases. The description of the test cases follows.

Each test case consists of two lines.

The first line contains a single even integer $$$n$$$ $$$(2 \le n \le 2\cdot10^5)$$$ — the size of the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ $$$(0 \le a_i \le 10^9)$$$ — the elements of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case print a single integer — the maximum score obtainable.

Example
Input
3
4
1 1 1 1
2
5 6
6
1 0 2 2 1 1
Output
2
4
4