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
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print values of nodes in the max-heap in order of their id (from $1$ to $H$).

class MaxHeap():
    def __init__(self, a, h):
        self.a = a
        self.h = h
    def parent(self, i):
        return i//2
        
    def left(self, i):
        return 2 * i

    def right(self, i):
        return 2 * i + 1

    def maxHeapify(self, a, i):
        l = self.left(i)
        r = self.right(i)
        if l <= self.h and a[l] > a[i]:
            largest = l
        else:
            largest = i
        if r <= self.h and a[r] > a[largest]:
            largest = r
        if largest != i:
            a[i], a[largest] = a[largest], a[i]
            self.maxHeapify(a, largest)

    def buildMaxHeap(self, a):
        for i in range(self.h//2, 0, -1):
            self.maxHeapify(a, i)
        return a

if __name__ == '__main__':
    n = int(input().rstrip())
    a = [-1]
    a += [int(i) for i in input().rstrip().split(" ")]
    x = MaxHeap(a, n)
    for i in x.buildMaxHeap(x.a)[1:]:
        print("", i, end = "")
    print()