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:
import sys
import math
import bisect

def solve(A):
    n = len(A)
    A.sort()
    '''
    print('n: %d' % (n))
    print('A: %s' % (str(A)))
    '''
    B = []
    if n % 2 == 0:
        i = (n - 1) // 2
        j = i + 1
        while i >= 0 and j < n:
            #print('i: %d, j: %d' % (i, j))
            B.append(A[i])
            B.append(A[j])
            i -= 1
            j += 1
    else:
        mid = (n - 1) // 2
        B.append(A[mid])
        i = mid - 1
        j = mid + 1
        while i >= 0 and j < n:
            #print('i: %d, j: %d' % (i, j))
            B.append(A[i])
            B.append(A[j])
            i -= 1
            j += 1
    return B

def main():
    for _ in range(int(input())):
        n = int(input())
        A = list(map(int, input().split()))
        A = solve(A)
        print(' '.join(list(str(a) for a in A)))

if __name__ == "__main__":
    main()