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 sys,math 
def binarySearch(arr, l, r, x): 
    ans=-1
    while l <= r: 
  
        mid = l + (r - l)//2; 
          
        # Check if x is present at mid 
        if arr[mid] == x: 
            ans=mid
            return ans
        # If x is greater, ignore left half 
        elif arr[mid] < x: 
            ans=mid
            l = mid + 1
  
        # If x is smaller, ignore right half 
        else: 
            
            r = mid - 1
      
    # If we reach here, then the element was not present 
    return ans
t=int(sys.stdin.readline())
for _ in range(t):
    n=int(sys.stdin.readline())
    a=list(map(int,sys.stdin.readline().split()))
    a.sort()
    l=0
    r=n-1
    ans=[0]*n
    for i in range(n-1,-1,-1):
        if(i&1):
            ans[i]=a[r];
            r-=1
        else:
            ans[i]=a[l];
            l+=1
        
    print(*ans)