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:
def solve (n,k) :
    k.sort()
    mid = n//2
    state = 0
    if n%2 == 0 :
        pointer1 = mid-1
        pointer2 = mid
    else :
        pointer1 = mid-1
        pointer2 = mid+1
        
        diff1 = abs(k[pointer1]-k[mid])
        diff2 = abs(k[pointer2]-k[mid])
        
        if diff2 > diff1 :
            print (k[mid],k[pointer1],k[pointer2],end=" ")
            
        else :
            print (k[mid],k[pointer2],k[pointer1],end=" ")
            state = 1
        pointer1 -= 1
        pointer2 += 1
    
    while pointer1 >= 0 and pointer2 < n :
        if state == 0 :
            print(k[pointer1],k[pointer2],end=" ")
            
        else :
            print(k[pointer2],k[pointer1],end=" ")
            
        pointer1 -= 1
        pointer2 += 1
    
    print("")
    
        
        
              

n = int(input())

for x in range(n) :
    x = int(input())
    seq2 = list(map(int,input().split()))

    solve(x,seq2)