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
def swap(a: list, aux, i, j):
    a[j] = a[i]
    a[i] = aux


def z_sort(n: int, a: list):
    a = sorted(a)
    j = 1
    for i in range(2, n, 2):
        if a[i] > a[i - 1]:
            swap(a, a[j], i, j)
            j += 2

    for i in range(n - 1):
        print(a[i], end=' ')
    print(a[n - 1])


def main():
    n = int(input())
    a = list(map(int, input().split()))
    z_sort(n, a)


if __name__ == '__main__':
    main()
			  	 	  			 			  	 			  	