A student of z-school found a kind of sorting called z-sort. The array a with n elements are z-sorted if two conditions hold:

  1. ai ≥ ai - 1 for all even i, 
  2. ai ≤ ai - 1 for all odd i > 1. 



For example the arrays [1,2,1,2] and [1,1,1,1] are z-sorted while the array [1,2,3,4] isn’t z-sorted.

Can you make the array z-sorted?

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of elements in the array a.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

If it's possible to make the array a z-sorted print n space separated integers ai — the elements after z-sort. Otherwise print the only word "Impossible".

Examples

Input

4
1 2 2 1


Output

1 2 1 2


Input

5
1 3 2 2 5


Output

1 5 2 3 2
#include <bits/stdc++.h>
void swap(int *a, int *b);
int main(void) {
  int numCount;
  scanf("%d", &numCount);
  int num[numCount];
  for (int i = 0; i < numCount; i++) {
    scanf("%d", &num[i]);
  }
  for (int i = 0; i < numCount; i++) {
    for (int j = 0; j < numCount - 1; j++) {
      if (num[j] > num[j + 1]) {
        swap(&num[j], &num[j + 1]);
      }
    }
  }
  int flag = 1;
  for (int i = 0; i < numCount; i++) {
    int counter = 0;
    if (i % 2 == 0 && i > 0) {
      if (num[numCount - counter - 1] < num[counter]) {
        flag = 0;
      }
      counter++;
    } else {
      if (num[counter] > num[numCount - counter - 1]) {
        flag = 0;
      }
    }
  }
  if (flag == 1) {
    int ctr = 0;
    for (int i = 0; i < numCount; i++) {
      if (i % 2 == 0) {
        printf("%d ", num[ctr]);
        ctr++;
      } else if (i % 2 == 1) {
        printf("%d ", num[numCount - ctr]);
      }
    }
    puts("");
  } else {
    printf("Impossible\n");
  }
  return 0;
}
void swap(int *a, int *b) {
  int temp = *a;
  *a = *b;
  *b = temp;
  return;
}
