#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
template <class T>
T maxt(T x, T y) {
  if (x > y)
    return x;
  else
    return y;
}
template <class T>
T mint(T x, T y) {
  if (x > y)
    return y;
  else
    return x;
}
double print_double(double d) { printf("%.11f", d); }
vector<long long> divisor(long long n) {
  vector<long long> ret;
  for (long long i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n) ret.push_back(n / i);
    }
  }
  sort(begin(ret), end(ret));
  return (ret);
}
struct edge {
  int from;
  int to;
  long long cost;
};
vector<long long> bellman_ford(vector<edge> edges, int V, int E, int r,
                               long long INF = 100000000000) {
  vector<long long> cost_to(V, INF);
  cost_to[r] = 0;
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < E; j++) {
      edge e = edges[j];
      if (cost_to[e.from] == INF) continue;
      if (cost_to[e.to] > cost_to[e.from] + e.cost) {
        cost_to[e.to] = cost_to[e.from] + e.cost;
        if (i == V - 1) {
          printf("NEGATIVE CYCLE\n");
          return {};
        }
      }
    }
  }
  return cost_to;
}
const int MAX = 510000;
const int MOD = 1000000007;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}
long long COM(int n, int k) {
  if (n < k) return 0;
  if (n < 0 || k < 0) return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
int main() {
  int t, n;
  scanf("%d", &t);
  for (int i = 0; i < t; i++) {
    scanf("%d", &n);
    vector<long long> A(n);
    for (int j = 0; j < n; j++) scanf("%lld", &A[j]);
    sort(A.begin(), A.end());
    vector<long long> ans;
    if (A.size() % 2) ans.push_back(A[n - 1]);
    for (int j = 0; j < n / 2; j++) {
      ans.push_back(A[j]);
      ans.push_back(A[n / 2 * 2 - 1 - j]);
    }
    for (int j = 0; j < n; j++) printf("%d ", ans[n - 1 - j]);
    printf("\n");
  }
}

### Prompt

Create a solution in CPP for the following 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".

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
template <class T>
T maxt(T x, T y) {
  if (x > y)
    return x;
  else
    return y;
}
template <class T>
T mint(T x, T y) {
  if (x > y)
    return y;
  else
    return x;
}
double print_double(double d) { printf("%.11f", d); }
vector<long long> divisor(long long n) {
  vector<long long> ret;
  for (long long i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n) ret.push_back(n / i);
    }
  }
  sort(begin(ret), end(ret));
  return (ret);
}
struct edge {
  int from;
  int to;
  long long cost;
};
vector<long long> bellman_ford(vector<edge> edges, int V, int E, int r,
                               long long INF = 100000000000) {
  vector<long long> cost_to(V, INF);
  cost_to[r] = 0;
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < E; j++) {
      edge e = edges[j];
      if (cost_to[e.from] == INF) continue;
      if (cost_to[e.to] > cost_to[e.from] + e.cost) {
        cost_to[e.to] = cost_to[e.from] + e.cost;
        if (i == V - 1) {
          printf("NEGATIVE CYCLE\n");
          return {};
        }
      }
    }
  }
  return cost_to;
}
const int MAX = 510000;
const int MOD = 1000000007;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}
long long COM(int n, int k) {
  if (n < k) return 0;
  if (n < 0 || k < 0) return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
int main() {
  int t, n;
  scanf("%d", &t);
  for (int i = 0; i < t; i++) {
    scanf("%d", &n);
    vector<long long> A(n);
    for (int j = 0; j < n; j++) scanf("%lld", &A[j]);
    sort(A.begin(), A.end());
    vector<long long> ans;
    if (A.size() % 2) ans.push_back(A[n - 1]);
    for (int j = 0; j < n / 2; j++) {
      ans.push_back(A[j]);
      ans.push_back(A[n / 2 * 2 - 1 - j]);
    }
    for (int j = 0; j < n; j++) printf("%d ", ans[n - 1 - j]);
    printf("\n");
  }
}

```