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:
from copy import deepcopy
t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int,input().split()))
    b = deepcopy(a)
    b.sort(reverse=True)
    a.sort()
    c = [0]*n
    if n%2==0:
        i=n-1
        j =0
        while(i>=0):
            c[i] = a[j]
            c[i-1] = b[j]
            i -= 2
            j += 1
    else:
        i=n-1
        j =0
        while(i>0):
            c[i] = a[j]
            c[i-1] = b[j]
            i-=2
            j+=1
        c[0] = a[j]
    # i=n-1
    # while(i>=0):
    #     c[i] = a[n-1-i]
    #     i -= 1
    #     if i>=0:
    #         c[i] = b[n-i]
    #         i -= 1
    # for i in range(n//2):
    #     c[n-1-i] = a[i]
    #     if n-2-i>=0:
    #         c[n-2-i] = b[i]
    # if n%2==1:
    #     c.pop()
    print(*c)