CodeForces - 652B

B. z-sort

time limit per test 1 second  memory limit per test  256 megabytes

input

standard input

output

standard output

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. a_i ≥ a_i - 1 for all even i,
2. a_i ≤ a_i - 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 a_i (1 ≤ a_i ≤ 10⁹) — the elements of the array a.

Output

If it's possible to make the array a z-sorted print n space separated integers a_i — 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<stdio.h>
#include<algorithm>
using namespace std;
#define N 1005
int a[N];
int main()
{
	int n;
	while(~scanf("%d",&n)){
		for(int i = 1;i <= n;i++){
			scanf("%d",&a[i]);
		}
		sort(a+1,a+n+1);
		int l = (n+1)/2+1,len =1 ;
		for(int i = 1;i <= n;i++){
			if(i&1)
			printf("%d ",a[len++]);
			else
			printf("%d ",a[l++]);
	}
	printf("\n");
}
return 0;
}