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

input = sys.stdin.readline

def inp():
    return(int(input()))

def inlt():
    return(list(map(int,input().split())))

# def foo(n):
#     print()

results = []

for t in range(inp()):
    length = inp()
    arr = inlt()
    arr = sorted(arr)
    res = []

    left = 0
    right = length-1
    while left<=right:
        res.append(arr[right])
        if left!=right:
            res.append(arr[left])
        left+=1
        right-=1

    results.append(res)

for r in results:
    x=' '.join([str(a) for a in r[::-1]])
    print(x)






# def eratosthenes(n):
#     multiples = set()
#     for i in range(2, n+1):
#         if i not in multiples:
#             yield i
#             multiples.update(range(i*i, n+1, i))
#
# primes = (list(eratosthenes(1000)))
#
# print(primes)