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 math
def facts(n):
    ans = []
    for i in range(2, int(math.sqrt(n)+1)):
        if(n%i==0):
            ans.append(i)
            ans.append(n//i)
    ans = sorted(ans)
    return ans

for _ in range(int(input())):
    n = int(input())
    nms = sorted(list(map(int, input().split())))
    pnt1, pnt2 = 0, n-1
    ans = []
    if(n%2==1):
        while(pnt1<=pnt2):
            if(pnt1==pnt2):
                ans.append(str(nms[pnt1]))
            else:
                ans.append(str(nms[pnt2]))
                ans.append(str(nms[pnt1]))
            pnt2-=1
            pnt1+=1
    else:
        while(pnt1<pnt2):
            ans.append(str(nms[pnt2]))
            ans.append(str(nms[pnt1]))
            pnt2-=1
            pnt1+=1
    ans = ans[::-1]
    print(' '.join(ans))