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() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    vector<long long int> v(n);
    for (long long int i = 0; i < n; i++) {
      cin >> v[i];
    }
    sort(v.begin(), v.end());
    long long int t = (n - 1) / 2;
    vector<long long int> vv(n + 1);
    vv[1] = v[t];
    if (n % 2 == 1) {
      for (long long int i = 1; i <= n - 1; i++) {
        if (i % 2 == 1) {
          vv[i + 1] = v[t + i];
          t = t + i;
        } else {
          vv[i + 1] = v[t - i];
          t = t - i;
        }
      }
    } else {
      for (long long int i = 1; i <= n - 2; i++) {
        if (i % 2 == 1) {
          vv[i + 1] = v[t + i];
          t += i;
        } else {
          vv[i + 1] = v[t - i];
          t -= i;
        }
      }
      vv[n] = v[n - 1];
    }
    for (long long int i = 1; i <= n; i++) cout << vv[i] << " ";
    cout << "\n";
  }
  return 0;
}