p02288 Maximum Heap
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.

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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
```python
H = int(input())
A = [0]
for i in input().split(): A.append(int(i))

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

for i in range(1,H//2+1)[::-1]: maxHeapify(i)
for i in range(1,H+1): print(" {}".format(A[i]),end="")
print("")

```