human
A binary heap which satisfies max-heap property is called max-heap. In a max-heap, for every node $i$ other than the root, $A[i] \leq A[parent(i)]$, that is, the value of a node is at most the value of its parent. The largest element in a max-heap is stored at the root, and the subtree rooted at a node contains values no larger than that contained at the node itself.

Here is an example of a max-heap.



Write a program which reads an array and constructs a max-heap from the array based on the following pseudo code.

$maxHeapify(A, i)$ move the value of $A[i]$ down to leaves to make a sub-tree of node $i$ a max-heap. Here, $H$ is the size of the heap.

1  maxHeapify(A, i)
2      l = left(i)
3      r = right(i)
4      // select the node which has the maximum value
5      if l ≤ H and A[l] > A[i]
6          largest = l
7      else
8          largest = i
9      if r ≤ H and A[r] > A[largest]
10         largest = r
11
12     if largest ≠ i　// value of children is larger than that of i
13         swap A[i] and A[largest]
14         maxHeapify(A, largest) // call recursively

The following procedure buildMaxHeap(A) makes $A$ a max-heap by performing maxHeapify in a bottom-up manner.

1 buildMaxHeap(A)
2    for i = H/2 downto 1
3        maxHeapify(A, i)



Input

In the first line, an integer $H$ is given. In the second line, $H$ integers which represent elements in the binary heap are given in order of node id (from $1$ to $H$).

Output

Print values of nodes in the max-heap in order of their id (from $1$ to $H$). Print a single space character before each value.

Example

Input

10
4 1 3 2 16 9 10 14 8 7

Output

16 14 10 8 7 9 3 2 4 1
 What is a Python code to print values of nodes in the max-heap in order of their id (from $1$ to $H$)?
assistant
#Here is Python code to print values of nodes in the max-heap in order of their id (from $1$ to $H$).

import sys
input = lambda: sys.stdin.readline().rstrip() 
sys.setrecursionlimit(10**7)
INF = 10**10
def I(): return int(input())
def F(): return float(input())
def SS(): return input()
def LI(): return [int(x) for x in input().split()]
def LI_(): return [int(x)-1 for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LSS(): return input().split()

def resolve():
    H = I()
    A = [0]
    tmp = LI()
    for i in tmp:
        A.append(i)

    def maxHeapify(A, i):
        l = 2*i
        r = 2*i+1
        if l <= H and A[l] > A[i]:
            largest = l
        else:
            largest = i
        if r <= H and A[r] > A[largest]:
            largest = r

        if largest != i:
            A[i], A[largest] = A[largest], A[i]
            maxHeapify(A, largest)

    def buildMaxHeap(A):
        for i in range(H//2, 0, -1):
            maxHeapify(A, i)

    buildMaxHeap(A)

    ans = ''
    for i in range(1, H+1):
        ans += ' ' + str(A[i])
    print(ans)

if __name__ == '__main__':
    resolve()