human
Give me a Python code to print n space separated integers ai — the elements after z-sort given the following:
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
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print n space separated integers ai — the elements after z-sort.

class CodeforcesTask652BSolution:
    def __init__(self):
        self.result = ''
        self.n = 0
        self.array = []

    def read_input(self):
        self.n = int(input())
        self.array = [int(x) for x in input().split(" ")]

    def process_task(self):
        self.array.sort()
        result = []
        for x in range(self.n // 2):
            result.append(self.array[x])
            result.append(self.array[x + self.n // 2 + self.n % 2])
        if self.n % 2:
            result.append(self.array[self.n // 2])
        self.result = " ".join([str(x) for x in result])

    def get_result(self):
        return self.result

if __name__ == "__main__":
    Solution = CodeforcesTask652BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())