Problem: You have array of n numbers a_{1}, a_{2}, …, a_{n}. 

Rearrange these numbers to satisfy |a_{1} - a_{2}| ≤ |a_{2} - a_{3}| ≤ … ≤ |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 ≤ t ≤ 10^{4}) — the number of test cases.

The first line of each test case contains single integer n (3 ≤ n ≤ 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}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 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 ≤ |a_{2} - a_{3}| = 1 ≤ |a_{3} - a_{4}| = 2 ≤ |a_{4} - a_{5}| = 2 ≤ |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 ≤ |a_{2} - a_{3}| = 2 ≤ |a_{3} - a_{4}| = 4. There are other possible answers like "2 4 8 1".

Solution (in PYTHON3):

Solution:
# Contest No.: 633
# Problem No.: B
# Solver:      JEMINI
# Date:        20200412

import sys

def main():
    t = int(input())
    for _ in range(t):
        n = int(sys.stdin.readline().strip())
        nums = list(map(int, sys.stdin.readline().split()))
        nums.sort()
        ans = []
        leftFlag = None
        pos = None
        if n % 2:
            ans.append(nums[n // 2])
            pos = n // 2
            if abs(nums[n // 2] - nums[n // 2 + 1]) > abs(nums[n // 2] - nums[n // 2 - 1]):
                leftFlag = True
            else:
                leftFlag = False
        else:
            if abs(nums[n // 2] - nums[n // 2 + 1]) > abs(nums[n // 2 - 1] - nums[n // 2 - 2]):
                ans.append(nums[n // 2 - 1])
                pos = n // 2 - 1
                leftFlag = False
            else:
                ans.append(nums[n // 2])
                pos = n // 2
                leftFlag = True
        cnt = 1
        while cnt < n:
            if leftFlag:
                #print(nums[pos - cnt])
                ans.append(nums[pos - cnt])
                pos -= cnt
            else:
                #print(nums[pos + cnt])
                ans.append(nums[pos + cnt])
                pos += cnt
            leftFlag = not leftFlag
            cnt += 1
        for i in ans:
            print(i, end = " ")
        print("")
    return

if __name__ == "__main__":
    main()