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:
n = input()
 
 
for i in range(int(n)):
    input()
    arr = input().split()
    arr = list(map(int, arr))
 
    arr_asc = sorted(arr)
    
    arr_1 = []
    arr_des = sorted(arr,reverse=True)
    
    
    arr_out = []
    flag = 0
    if int(len(arr)) % 2 == 0:
        m = int(len(arr)/2)
    else:
        flag = 1
        m = int(len(arr)/2) + 1
    for i in range(m):
        arr_out.append(arr_asc[i])
        if flag == 1:
            if(i != m-1):
                 arr_out.append(arr_des[i])
        else:
            arr_out.append(arr_des[i])
    
        
    for i in range(len(arr_out)-1,-1,-1):
        
        arr_1.append(int(arr_out[i]))  
        print(int(arr_out[i]),end=" ")  
        
    if(int(n) > 1):    
        print("\n")