#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const long long linf = 0x3f3f3f3f3f3f3f3f;
const int inf = 0x3f3f3f3f;
const double eps = 1e-6;
template <typename S, typename T>
inline bool Min(S &a, const T &b) {
  return a > b ? a = b, true : false;
}
template <typename S, typename T>
inline bool Max(S &a, const T &b) {
  return a < b ? a = b, true : false;
}
template <typename S, typename T>
inline void Adm(S &a, const T &b) {
  a = (a + b) % mod;
  if (a < 0) a += mod;
}
template <typename S, typename T>
inline void Mum(S &a, const T &b) {
  a = 1LL * a * b % mod;
}
template <typename T>
inline T Gcd(T a, T b) {
  while (b) {
    T t = b;
    b = a % b;
    a = t;
  }
  return a;
}
template <typename T>
inline int BitCnt(T x) {
  int cnt = 0;
  while (x) ++cnt, x &= x - 1;
  return cnt;
}
template <typename T>
inline bool IsPri(T x) {
  if (x < 2) return false;
  for (T i = 2; i * i <= x; ++i)
    if (x % i == 0) return false;
  return true;
}
inline long long qpow(long long a, long long n) {
  long long t = 1;
  while (n) {
    if (n & 1) t = t * a % mod;
    a = a * a % mod, n >>= 1;
  }
  return t % mod;
}
void p_bit(long long x) { cout << bitset<32>(x) << ':' << x << endl; }
const int maxn = 2e5 + 10;
const int maxm = 2e5 + 10;
int ans[maxn], a[maxn];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + 1 + n);
    int l = 1, r = n;
    for (int i = 1; i <= n; i += 2) {
      ans[i] = a[r--];
      ans[i + 1] = a[l++];
    }
    reverse(ans + 1, ans + 1 + n);
    for (int i = 1; i <= n; i++) printf("%d ", ans[i]);
    printf("\n");
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
const int mod = 998244353;
const long long linf = 0x3f3f3f3f3f3f3f3f;
const int inf = 0x3f3f3f3f;
const double eps = 1e-6;
template <typename S, typename T>
inline bool Min(S &a, const T &b) {
  return a > b ? a = b, true : false;
}
template <typename S, typename T>
inline bool Max(S &a, const T &b) {
  return a < b ? a = b, true : false;
}
template <typename S, typename T>
inline void Adm(S &a, const T &b) {
  a = (a + b) % mod;
  if (a < 0) a += mod;
}
template <typename S, typename T>
inline void Mum(S &a, const T &b) {
  a = 1LL * a * b % mod;
}
template <typename T>
inline T Gcd(T a, T b) {
  while (b) {
    T t = b;
    b = a % b;
    a = t;
  }
  return a;
}
template <typename T>
inline int BitCnt(T x) {
  int cnt = 0;
  while (x) ++cnt, x &= x - 1;
  return cnt;
}
template <typename T>
inline bool IsPri(T x) {
  if (x < 2) return false;
  for (T i = 2; i * i <= x; ++i)
    if (x % i == 0) return false;
  return true;
}
inline long long qpow(long long a, long long n) {
  long long t = 1;
  while (n) {
    if (n & 1) t = t * a % mod;
    a = a * a % mod, n >>= 1;
  }
  return t % mod;
}
void p_bit(long long x) { cout << bitset<32>(x) << ':' << x << endl; }
const int maxn = 2e5 + 10;
const int maxm = 2e5 + 10;
int ans[maxn], a[maxn];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + 1 + n);
    int l = 1, r = n;
    for (int i = 1; i <= n; i += 2) {
      ans[i] = a[r--];
      ans[i + 1] = a[l++];
    }
    reverse(ans + 1, ans + 1 + n);
    for (int i = 1; i <= n; i++) printf("%d ", ans[i]);
    printf("\n");
  }
  return 0;
}

```