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B. Sorted Adjacent Differences

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have array of $$$n$$$ numbers $$$a_{1}, a_{2}, \ldots, a_{n}$$$.

Rearrange these numbers to satisfy $$$|a_{1} - a_{2}| \le |a_{2} - a_{3}| \le \ldots \le |a_{n-1} - a_{n}|$$$, where $$$|x|$$$ denotes absolute value of $$$x$$$. It's always possible to find such rearrangement.

Note that all numbers in $$$a$$$ are not necessarily different. In other words, some numbers of $$$a$$$ may be same.

You have to answer independent $$$t$$$ test cases.

Input

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

The first line of each test case contains single integer $$$n$$$ ($$$3 \le n \le 10^{5}$$$) — the length of array $$$a$$$. It is guaranteed that the sum of values of $$$n$$$ over all test cases in the input does not exceed $$$10^{5}$$$.

The second line of each test case contains $$$n$$$ integers $$$a_{1}, a_{2}, \ldots, a_{n}$$$ ($$$-10^{9} \le a_{i} \le 10^{9}$$$).

Output

For each test case, print the rearranged version of array $$$a$$$ which satisfies given condition. If there are multiple valid rearrangements, print any of them.

Example

Input

2 6 5 -2 4 8 6 5 4 8 1 4 2

Output

5 5 4 6 8 -2 1 2 4 8

Note

In the first test case, after given rearrangement, $$$|a_{1} - a_{2}| = 0 \le |a_{2} - a_{3}| = 1 \le |a_{3} - a_{4}| = 2 \le |a_{4} - a_{5}| = 2 \le |a_{5} - a_{6}| = 10$$$. There are other possible answers like "5 4 5 6 -2 8".

In the second test case, after given rearrangement, $$$|a_{1} - a_{2}| = 1 \le |a_{2} - a_{3}| = 2 \le |a_{3} - a_{4}| = 4$$$. There are other possible answers like "2 4 8 1".

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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