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:
"""
Author: Q.E.D
Time: 2020-04-12 10:37:49
"""

T = int(input())
for _ in range(T):
    n = int(input())
    a = list(map(int, input().split()))
    a = sorted(a)
    i = n // 2
    d = 0
    sgn = 1
    cnt = 0
    ans = []
    while cnt < n:
        # print(i)
        ans.append(a[i])
        cnt += 1
        d = (abs(d) + 1)
        sgn *= -1
        i += (sgn * d)
    diff = ans[1] - ans[0]
    # b = []
    # for i in range(1, n):
    #     assert abs(ans[i] - ans[i - 1]) >= diff
    #     diff = abs(ans[i] - ans[i - 1])
    #     b.append(diff)
    # print(b)
    print(' '.join(map(str, ans)))