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
t=int(input())
while t:
    n=int(input())
    l=list(map(int,input().split()))
    l1=[]
    tmp=0
    l.sort()
    if n%2!=0:
        i=math.floor(n/2)
        l1.append(l[i])
        j=i+1
        i-=1
    else:
        j =int(n/2)
        i=j-1
    while i>=0 and j<n:
        if n%2==0 and tmp==0:
            l1.append(l[i])
            l1.append(l[j])
        elif  (abs(l1[tmp]-l[i])<abs(l1[tmp]-l[j])): #and (abs(l1[tmp]-l1[tmp-1])>l[j]):
            tmp+=1
            l1.append(l[j])
            l1.append(l[i])
        else:
            tmp+=1
            l1.append(l[i])
            l1.append(l[j])
        tmp+=1
        i-=1
        j+=1
    while j<n:
        l1.append(l[j])
        tmp+=1
        j+=1
    # while i>=0:
    #     l1.append(l[i])
    #     tmp+=1
    #     i-=1
    print(*l1)
    t-=1