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:
a = [0] * 100005
b = [0] * 100005
t = int(input())
while t != 0:
    n = int(input())
    a = input().split()
    for i in range(n):
        a[i] = int(a[i])
    a.sort()
    b[n - 1] = a[0]
    b[n - 2] = a[n - 1]
    for i in range(1, n // 2):
        if abs(int(b[n - 2 * i]) - int(a[n - i - 1])) > abs(int(b[n - 2 * i]) - int(a[i])):
            b[n - 2 * i - 1] = a[n - i - 1]
            b[n - 2 * i - 2] = a[i]
        else:
            b[n - 2 * i - 1] = a[i]
            b[n - 2 * i - 2] = a[n - i - 1]
    if n % 2 == 1:
        b[0] = a[n // 2]
    for i in range(n):
        print(b[i], end = ' ')
        b[i] = 0
    print()
    t -= 1