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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t, i, j, k;
  cin >> t;
  for (j = 0; j < t; j++) {
    int n;
    cin >> n;
    int64_t a[n];
    vector<int64_t> v;
    for (i = 0; i < n; i++) {
      cin >> a[i];
    }
    sort(a, a + n);
    int l, r;
    if (n % 2 == 0) {
      l = n / 2 - 1;
      r = n / 2;
    } else {
      l = (n - 1) / 2;
      r = (n - 1) / 2;
    }
    while (l >= 0 && r < n) {
      if (l == r) {
        v.push_back(a[l]);
        l--;
        r++;
      } else {
        v.push_back(a[l]);
        v.push_back(a[r]);
        l--;
        r++;
      }
    }
    for (i = 0; i < v.size(); i++) {
      cout << v[i] << " ";
    }
    cout << endl;
  }
}