#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using ld = long double;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<double, double>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<double>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
template <class T>
using mpq = priority_queue<T, vector<T>, greater<T>>;
struct fhash {
  static uint64_t s(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t r =
        chrono::steady_clock::now().time_since_epoch().count();
    return s(x + r);
  }
};
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = (lo + hi) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = (lo + hi + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
const int di[4] = {-1, 0, 1, 0}, dj[4] = {0, 1, 0, -1};
const int di8[8] = {-1, -1, 0, 1, 1, 1, 0, -1},
          dj8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const int MOD = 1e9 + 7;
const ld PI = acos((ld)-1);
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) { return uniform_int_distribution<ll>(a, b)(rng); }
bool pow2(int i) { return i && (i & -i) == i; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
template <class T>
bool chmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool chmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
void remDup(vector<T>& v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p);
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p);
string to_string(char c) { return string(1, c); }
string to_string(bool b) { return to_string((int)b); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
string to_string(vb v) {
  string res = "{";
  for (int i = (0); i < (((int)(v).size())); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
string to_string(bitset<SZ> b) {
  string res = "";
  for (int i = (0); i < (((int)(b).size())); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p));
}
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p)) + " " + to_string(get<3>(p));
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p);
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p);
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T, size_t SZ>
void re(AR<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& d) {
  string t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  string t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.f, p.s);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(array<T, SZ>& x) {
  for (auto& a : x) re(a);
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p) {
  re(get<0>(p), get<1>(p), get<2>(p));
}
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p) {
  re(get<0>(p), get<1>(p), get<2>(p), get<3>(p));
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void IOS(int n = 10, string s = "") {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.precision(n);
  cerr.precision(n);
  cerr << fixed;
  cout << fixed;
  if (((int)(s).size())) {
    setIn(s + ".in"), setOut(s + ".out");
  }
}
void solve() {
  int n;
  re(n);
  vi a(n), ans;
  re(a);
  sort((a).begin(), (a).end());
  int l, r;
  if (n & 1) {
    ans.push_back(a[n / 2]);
    l = n / 2 - 1, r = n / 2 + 1;
  } else
    l = n / 2 - 1, r = n / 2;
  while (l >= 0 && r < n) {
    ans.push_back(a[l]);
    ans.push_back(a[r]);
    --l, ++r;
  }
  ps(ans);
}
int main() {
  IOS();
  int t = 1;
  re(t);
  for (int i = (0); i < (t); ++i) {
    solve();
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using ld = long double;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<double, double>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<double>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
template <class T>
using mpq = priority_queue<T, vector<T>, greater<T>>;
struct fhash {
  static uint64_t s(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t r =
        chrono::steady_clock::now().time_since_epoch().count();
    return s(x + r);
  }
};
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = (lo + hi) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = (lo + hi + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
const int di[4] = {-1, 0, 1, 0}, dj[4] = {0, 1, 0, -1};
const int di8[8] = {-1, -1, 0, 1, 1, 1, 0, -1},
          dj8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const int MOD = 1e9 + 7;
const ld PI = acos((ld)-1);
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) { return uniform_int_distribution<ll>(a, b)(rng); }
bool pow2(int i) { return i && (i & -i) == i; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
template <class T>
bool chmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool chmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
void remDup(vector<T>& v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p);
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p);
string to_string(char c) { return string(1, c); }
string to_string(bool b) { return to_string((int)b); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
string to_string(vb v) {
  string res = "{";
  for (int i = (0); i < (((int)(v).size())); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
string to_string(bitset<SZ> b) {
  string res = "";
  for (int i = (0); i < (((int)(b).size())); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p));
}
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p)) + " " + to_string(get<3>(p));
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p);
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p);
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T, size_t SZ>
void re(AR<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& d) {
  string t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  string t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.f, p.s);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(array<T, SZ>& x) {
  for (auto& a : x) re(a);
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p) {
  re(get<0>(p), get<1>(p), get<2>(p));
}
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p) {
  re(get<0>(p), get<1>(p), get<2>(p), get<3>(p));
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void IOS(int n = 10, string s = "") {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.precision(n);
  cerr.precision(n);
  cerr << fixed;
  cout << fixed;
  if (((int)(s).size())) {
    setIn(s + ".in"), setOut(s + ".out");
  }
}
void solve() {
  int n;
  re(n);
  vi a(n), ans;
  re(a);
  sort((a).begin(), (a).end());
  int l, r;
  if (n & 1) {
    ans.push_back(a[n / 2]);
    l = n / 2 - 1, r = n / 2 + 1;
  } else
    l = n / 2 - 1, r = n / 2;
  while (l >= 0 && r < n) {
    ans.push_back(a[l]);
    ans.push_back(a[r]);
    --l, ++r;
  }
  ps(ans);
}
int main() {
  IOS();
  int t = 1;
  re(t);
  for (int i = (0); i < (t); ++i) {
    solve();
  }
}

```