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 PYTHON):

Solution:
def solve(ns):
    ns.sort()
    n = len(ns)
    res = []
    p, q = 0, n - 1
    while p <= q:
        if p <= q:
            res.append(ns[q])
            q -= 1
        if p <= q:
            res.append(ns[p])
            p += 1
    return res[::-1]

def verify(ns):
    INF = 10 ** 10
    pre = -INF
    n = len(ns)
    for i in xrange(1, n):
        assert abs(ns[i] - ns[i - 1]) >= pre
        pre = abs(ns[i] - ns[i - 1])
    return True

def test():
    from random import randint
    for i in xrange(100):
        n = randint(1, 200)
        ns = [randint(-100, 100) for i in xrange(n)]
        res = solve(ns)
        assert verify(res)


T = int(raw_input())

for case_ in xrange(T):
    n = int(raw_input())
    ns = map(int, raw_input().split())
    res = solve(ns)
    for item in res:
        print item,
    print ''