[CodeForces

Link：http://codeforces.com/problemset/problem/652/B

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. 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

41 2 2 1

output

1 2 1 2

input

51 3 2 2 5

output

1 5 2 3 2

Code:

#include<cstdio>#include<cstdlib>#include<cmath>#include<cstring>#include<algorithm>#include<iostream>#include<queue>#include<stack>using namespace std;int a[1005],b[1005];int main(){int n;while(~scanf("%d",&n)){for(int i=1;i<=n;i++)scanf("%d",&a[i]);int k=1;sort(a+1,a+1+n);for(int i=1;i<=n;i+=2)b[i]=a[k++];  //所有奇数位上的数都小于上一个数for(int i=2;i<=n;i+=2)b[i]=a[k++];  //所有偶数位上的数都大于上一个数for(int i=1;i<=n;i++)printf("%d%c",b[i],i==n? '\n':' ');}return 0;}