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
#!/usr/bin/python3
# -*- config:utf-8 -*-

import sys

# get source data
def getSrcData():
    f = sys.stdin
    buf = f.read()
    buf=buf.split('\n')
    cnt=int(buf[0])
    if cnt!=0:
        src=buf[1].split(' ')
        src=[int(i) for i in src]
    else:
        src=[]
    return cnt,src

# find transform to zsort
def getTransform(cnt,src):
    src.sort()
    result=[]
    for i in range(0,cnt//2):
        result.append(src[i])
        result.append(src[cnt-1-i])
    if cnt%2==1:
        result.append(src[cnt//2])
    return result

# save result
def saveResult(result):
    if len(result)==0:
        pbuf='Impossible'
    else:
        pbuf=[str(i) for i in result]
        pbuf=' '.join(pbuf)
    f = sys.stdout
    f.write(pbuf)
    f.flush()

# start
def run():
    cnt,src=getSrcData()
    if cnt!=0:
        result=getTransform(cnt,src)
    else:
        result=[]
    saveResult(result)

if __name__ == '__main__':
    run()
