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:
from math import ceil, sqrt, floor, sqrt

# import sys
# sys.setrecursionlimit(50000)

import collections
from typing import List
from fractions import gcd

from collections import deque


# 1.5m recursive solution
# 7m submit WA

# 4m approach
# 16m submit

from collections import Counter, deque


t = int(input())

for _ in range(t):
    n = int(input())
    A = list(map(int, input().split()))

    A.sort()

    res = [0] * n
    if n % 2 == 1:
        res[0] = A[n // 2]
        for i in range(n // 2):
            res[2*i+1] = A[n // 2 + i + 1]
            res[2*i+2] = A[n // 2 - i - 1]
        print(' '.join(str(c) for c in res))
    else:
        for i in range(n // 2):
            res[2*i] = A[n // 2 + i]
            res[2*i+1] = A[n // 2 - i - 1]
        print(' '.join(str(c) for c in res))