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 PYTHON):

Solution:


def sorted_diffs(arr):

    arr.sort()
    out = []

    left = list(reversed(arr[:len(arr)//2]))
    right = arr[len(arr)//2:]

    for i in range(len(arr)//2):
        out.append(right[i])
        out.append(left[i])

    if len(arr)%2 == 1:
        out.append(right[-1])

    return out

def check(arr, init):

    from collections import Counter

    ca = Counter(arr)
    ci = Counter(init)

    for i, c in ca.items():
        if ci[i] != c:
            print 'Different arrays %s' % i
            return False

    for i in range(1, len(arr)-1):
        if abs(arr[i-1] - arr[i]) > abs(arr[i] - arr[i+1]):
            print 'Failed at %s' % i
            ds = []
            for j in range(1, len(arr)):
                ds.append(abs(arr[j-1]-arr[j]))

            print ' '.join(map(str, ds))
            return False
    return True

# import random

# for i in range(3, 100000):
    # for _ in range(10):
        # arr = [random.randint(3, 1000) for _ in range(i+1)]

        # out_arr = sorted_diffs(arr)
        # if not check(out_arr, arr):
            # print 'NOT OK: i=%s, arr=%s, out_arr=%s' % (i, arr, out_arr)
            # import sys
            # sys.exit(1)
        # else:
            # print 'OK: %s' % i

tests = int(input())

for _ in range(tests):
    input()
    arr = list(map(int, raw_input().split(' ')))

    out_arr = sorted_diffs(arr)
    print ' '.join(map(str, out_arr))