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:
'''input
3
6
5 -2 4 8 6 5
4
8 1 4 2
5
1 3 7 5 4
'''

import sys
import math
from collections import Counter

debug = 1
readln = sys.stdin.readline
#sys.setrecursionlimit(1000000)

def write(s):
    sys.stdout.write(str(s))

def writeln(s):
    sys.stdout.write(str(s))
    sys.stdout.write('\n')

def readint():
    return int(readln().strip())

def readints():
    return map(int, readln().split())

def readstr():
    return readln().strip()

def readstrs():
    return readln().split()

def dbg(*args):
    if debug: print(' '.join(map(str, args)))

def solve(n, A):
    A = sorted(A)
    mid = n // 2
    ret = [A[mid]]
    for i in range(1, n):
        valid = 0
        if mid - i >= 0:
            ret.append(A[mid-i])
            valid = 1

        if mid + i < n:
            ret.append(A[mid+i])
            valid = 1
        if not valid: return ret

    return 0

t = readint()
for _ in range(t):
    n = readint()
    A = readints()
    writeln(' '.join(map(str, solve(n, A))))