Cowboy Vlad has a birthday today! There are n children who came to the celebration. In order to greet Vlad, the children decided to form a circle around him. Among the children who came, there are both tall and low, so if they stand in a circle arbitrarily, it may turn out, that there is a tall and low child standing next to each other, and it will be difficult for them to hold hands. Therefore, children want to stand in a circle so that the maximum difference between the growth of two neighboring children would be minimal possible.

Formally, let's number children from 1 to n in a circle order, that is, for every i child with number i will stand next to the child with number i+1, also the child with number 1 stands next to the child with number n. Then we will call the discomfort of the circle the maximum absolute difference of heights of the children, who stand next to each other.

Please help children to find out how they should reorder themselves, so that the resulting discomfort is smallest possible.

Input

The first line contains a single integer n (2 ≤ n ≤ 100) — the number of the children who came to the cowboy Vlad's birthday.

The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) denoting heights of every child.

Output

Print exactly n integers — heights of the children in the order in which they should stand in a circle. You can start printing a circle with any child.

If there are multiple possible answers, print any of them.

Examples

Input


5
2 1 1 3 2


Output


1 2 3 2 1


Input


3
30 10 20


Output


10 20 30

Note

In the first example, the discomfort of the circle is equal to 1, since the corresponding absolute differences are 1, 1, 1 and 0. Note, that sequences [2, 3, 2, 1, 1] and [3, 2, 1, 1, 2] form the same circles and differ only by the selection of the starting point.

In the second example, the discomfort of the circle is equal to 20, since the absolute difference of 10 and 30 is equal to 20.
#include <bits/stdc++.h>
using namespace std;
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
inline long long toLongLong(string s) {
  long long v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
inline vector<char> toVC(string s) {
  vector<char> data(s.begin(), s.end());
  return data;
}
template <typename List>
void SPRIT(const std::string &s, const std::string &delim, List &result) {
  result.clear();
  string::size_type pos = 0;
  while (pos != string::npos) {
    string::size_type p = s.find(delim, pos);
    if (p == string::npos) {
      result.push_back(s.substr(pos));
      break;
    } else {
      result.push_back(s.substr(pos, p - pos));
    }
    pos = p + delim.size();
  }
}
vector<string> SPRIT(const std::string &s, const std::string &delim) {
  vector<string> result;
  string::size_type pos = 0;
  while (pos != string::npos) {
    string::size_type p = s.find(delim, pos);
    if (p == string::npos) {
      result.push_back(s.substr(pos));
      break;
    } else {
      result.push_back(s.substr(pos, p - pos));
    }
    pos = p + delim.size();
  }
  return result;
}
string TRIM(const string &str, const char *trimCharacterList = " \t\v\r\n") {
  string result;
  string::size_type left = str.find_first_not_of(trimCharacterList);
  if (left != string::npos) {
    string::size_type right = str.find_last_not_of(trimCharacterList);
    result = str.substr(left, right - left + 1);
  }
  return result;
}
string REPLACE_STRING(const string source, const string find,
                      const string alt) {
  string result = source;
  string::size_type pos = 0;
  while (pos = result.find(find, pos), pos != string::npos) {
    result.replace(pos, find.length(), alt);
    pos += alt.length();
  }
  return result;
}
template <typename T>
bool VECTOR_EXISTS(vector<T> vec, T data) {
  auto itr = std::find(vec.begin(), vec.end(), data);
  size_t index = distance(vec.begin(), itr);
  if (index != vec.size())
    return true;
  else
    return false;
}
template <typename T>
vector<T> VECTOR_UNIQUE_ERASE(vector<T> vec) {
  sort(vec.begin(), vec.end());
  vec.erase(unique(vec.begin(), vec.end()), vec.end());
  return vec;
}
template <typename T>
void VECTOR_REMOVE_VALUE_ALL(vector<T> &vec, T data) {
  vec.erase(remove(vec.begin(), vec.end(), data), vec.end());
}
template <typename T>
vector<T> VECTOR_REMOVE_VALUE_ALL_FAST(vector<T> vec, T data) {
  vector<T> vec2;
  for (auto &x : vec)
    if (x != data) vec2.push_back(x);
  return vec2;
}
bool REG_MATCH(string const &text, regex const &re) {
  bool result = regex_match(text, re);
  return result;
}
bool REG_MATCH(string const &text, smatch &match, regex const &re) {
  bool result = regex_match(text, match, re);
  return result;
}
smatch REG_SEARCH(string const &text, regex const &re) {
  smatch m;
  regex_search(text, m, re);
  return m;
}
vector<smatch> REG_ALL_SEARCH(string const &text, regex const &re) {
  vector<smatch> matchs;
  sregex_iterator iter(text.cbegin(), text.cend(), re);
  sregex_iterator end;
  for (; iter != end; iter++) matchs.push_back(*iter);
  return matchs;
}
string REG_REPLACE(string const &text, regex const &re, string const &replace) {
  string result =
      regex_replace(text, re, replace, regex_constants::format_first_only);
  return result;
}
string REG_ALL_REPLACE(string const &text, regex const &re,
                       string const &replace) {
  string result = regex_replace(text, re, replace);
  return result;
}
template <typename T, typename U, typename V, typename W>
auto operator+(const std::pair<T, U> &l, const std::pair<V, W> &r)
    -> std::pair<decltype(l.first + r.first), decltype(l.second + r.second)> {
  return {l.first + r.first, l.second + r.second};
}
template <typename T, typename U, typename V, typename W>
auto operator-(const std::pair<T, U> &l, const std::pair<V, W> &r)
    -> std::pair<decltype(l.first - r.first), decltype(l.second - r.second)> {
  return {l.first - r.first, l.second - r.second};
}
double ceil_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(long long)(dOut + 0.9);
  return dOut * pow(10.0, -nLen);
}
double floor_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(long long)(dOut);
  return dOut * pow(10.0, -nLen);
}
double round_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(long long)(dOut + 0.5);
  return dOut * pow(10.0, -nLen);
}
int take_a_n(long long num, int n) {
  string str = toString(num);
  return str[str.length() - n] - '0';
}
long long bitcount64(long long bits) {
  bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
  bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
  bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
  bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
  bits = (bits & 0x0000ffff0000ffff) + (bits >> 16 & 0x0000ffff0000ffff);
  return (bits & 0x00000000ffffffff) + (bits >> 32 & 0x00000000ffffffff);
}
template <typename T1, typename T2>
inline void S_MAX(T1 &a, T2 b) {
  a = ((a) > (b) ? (a) : (b));
};
template <typename T1, typename T2>
inline void S_MIN(T1 &a, T2 b) {
  a = ((a) < (b) ? (a) : (b));
};
template <typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
  in >> p.first >> p.second;
  return in;
}
template <typename T>
istream &operator>>(istream &in, vector<T> &v) {
  for (auto &x : v) in >> x;
  return in;
}
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
template <typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
  if (min <= aim && aim <= max) {
    return true;
  } else {
    return false;
  }
}
template <typename T1, typename T2>
inline bool IS_OUT(const T1 toY, const T1 toX, const T2 H, const T2 W) {
  return (toY < 0 || toY >= H || toX < 0 || toX >= W);
}
template <class T>
inline T SQR(const T x) {
  return x * x;
}
template <class T1, class T2>
inline T1 POW(const T1 x, const T2 y) {
  if (!y)
    return 1;
  else if ((y & 1) == 0) {
    return SQR(POW(x, y >> 1));
  } else
    return POW(x, y ^ 1) * x;
}
template <typename T>
constexpr T ABS(T x) {
  return x < 0 ? -x : x;
}
template <class Iter>
bool next_partial_permutation(Iter first, Iter middle, Iter last) {
  reverse(middle, last);
  return next_permutation(first, last);
}
template <class Iter>
bool next_combination(Iter first1, Iter last1, Iter first2, Iter last2) {
  if ((first1 == last1) || (first2 == last2)) {
    return false;
  }
  Iter m1 = last1;
  Iter m2 = last2;
  --m2;
  while (--m1 != first1 && !(*m1 < *m2)) {
  }
  bool result = (m1 == first1) && !(*first1 < *m2);
  if (!result) {
    while (first2 != m2 && !(*m1 < *first2)) {
      ++first2;
    }
    first1 = m1;
    std::iter_swap(first1, first2);
    ++first1;
    ++first2;
  }
  if ((first1 != last1) && (first2 != last2)) {
    m1 = last1;
    m2 = first2;
    while ((m1 != first1) && (m2 != last2)) {
      std::iter_swap(--m1, m2);
      ++m2;
    }
    std::reverse(first1, m1);
    std::reverse(first1, last1);
    std::reverse(m2, last2);
    std::reverse(first2, last2);
  }
  return !result;
}
template <typename T>
constexpr bool ODD(T x) {
  return x % 2 != 0;
}
template <typename T>
constexpr bool EVEN(T x) {
  return x % 2 == 0;
}
template <class T>
inline T GCD(const T x, const T y) {
  if (x < 0) return GCD(-x, y);
  if (y < 0) return GCD(x, -y);
  return (!y) ? x : GCD(y, x % y);
}
template <class T>
inline T LCM(const T x, const T y) {
  if (x < 0) return LCM(-x, y);
  if (y < 0) return LCM(x, -y);
  return x * (y / GCD(x, y));
}
template <class T>
inline T EXTGCD(const T a, const T b, T &x, T &y) {
  if (a < 0) {
    T d = EXTGCD(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = EXTGCD(a, -b, x, y);
    y = -y;
    return d;
  }
  if (!b) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = EXTGCD(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline bool ISPRIME(const T x) {
  if (x <= 1) return false;
  for (T i = 2; i * i <= x; i++)
    if (x % i == 0) return false;
  return true;
}
template <class T>
vector<bool> ERATOSTHENES(const T n) {
  vector<bool> arr(n + 1, true);
  arr[0] = arr[1] = false;
  for (long long i = 2; i * i <= n; i++) {
    if (arr[i]) {
      for (long long j = i * 2LL; j <= n; j += i) {
        arr[j] = false;
      }
    }
  }
  return arr;
}
template <typename T>
vector<bool> ERATOSTHENES(const T a, const T b) {
  vector<bool> small = ERATOSTHENES(b);
  vector<bool> prime(b - a, true);
  for (long long i = 2; i * i <= b; i++) {
    if (small[i]) {
      for (long long j = max(2LL, (a + i - 1) / i) * i; j < b; j += i) {
        prime[j - a] = false;
      }
    }
  }
  return prime;
}
template <typename T>
vector<T> DIVISOR(T n) {
  vector<T> v;
  for (long long i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      v.push_back(i);
      if (i != n / i) {
        v.push_back(n / i);
      }
    }
  }
  sort(v.begin(), v.end());
  return v;
}
template <typename T>
vector<vector<T>> DIVISOR_ALL(T n) {
  vector<vector<T>> res(n + 1);
  for (long long i = 1; i <= n; i++) {
    for (long long j = i; j <= n; j += i) {
      res[j].push_back(i);
    }
  }
  return res;
}
template <typename T>
vector<pair<T, long long>> FACTORIZATION(T x) {
  vector<pair<T, long long>> ans;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      long long count = 0;
      while (x % i == 0) {
        count++;
        x /= i;
      }
      ans.push_back(make_pair(i, count));
    }
  }
  if (x != 1) ans.push_back(make_pair(x, 1));
  return ans;
}
long long POW_MOD(long long N, long long P, long long M) {
  if (P == 0) return 1LL;
  if (P % 2 == 0) {
    long long ret = POW_MOD(N, P / 2, M);
    return ret * ret % M;
  }
  return N * POW_MOD(N, P - 1, M) % M;
}
template <typename T>
inline T NCR(T n, T r) {
  if (r > n - r) r = n - r;
  T ans = 1;
  for (long long i = 0; i < long long(r); ++i) {
    ans = ans * (n - i) / (i + 1);
  }
  return ans;
}
long long NCR_MOD(long long n, long long r, long long M) {
  if (r > n - r) return NCR_MOD(n, n - r, M);
  long long numerator = 1LL;
  long long denominator = 1LL;
  for (long long i = 0; i < r; i++) {
    numerator *= (n - i);
    numerator %= M;
    denominator *= (i + 1);
    denominator %= M;
  }
  return numerator * POW_MOD(denominator, M - 2, M) % M;
}
int main() {
  int N;
  cin >> N;
  vector<long long> a(N);
  cin >> a;
  sort((a).begin(), (a).end());
  for (int i = 0; i < a.size(); i++) cout << a[i] << " ";
  return 0;
}
