#include <stdio.h>
#define MAX 500000
int A[MAX];
int H;
void maxheap(int *,int);

int main(){
int i;
  scanf("%d",&H);
  for (i = 1; i <= H; i++ ) {
    scanf("%d",&A[i]);
  }
  for (i = H/2 ; i > 0 ; i-- ){
    maxheap(A,i);
  }
  for (i=1 ; i<=H ;i++){
    printf(" %d",A[i]);
  }
  puts("");

  return 0;

}

void maxheap(int A[],int i){

  int l,r;
  int large,temp;

  l=i*2;
  r=i*2+1;

  if (l<=H && A[l]>A[i])large=l;
  else large=i;

  if (r<=H && A[r]>A[large])large=r;

  if(large!=i){
    temp=A[i];
    A[i]=A[large];
    A[large]=temp;
    maxheap(A,large);
  }
}
### Prompt

Your challenge is to write a cpp solution to the following problem:

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.

<image>


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

### Response

```cpp
#include <stdio.h>
#define MAX 500000
int A[MAX];
int H;
void maxheap(int *,int);

int main(){
int i;
  scanf("%d",&H);
  for (i = 1; i <= H; i++ ) {
    scanf("%d",&A[i]);
  }
  for (i = H/2 ; i > 0 ; i-- ){
    maxheap(A,i);
  }
  for (i=1 ; i<=H ;i++){
    printf(" %d",A[i]);
  }
  puts("");

  return 0;

}

void maxheap(int A[],int i){

  int l,r;
  int large,temp;

  l=i*2;
  r=i*2+1;

  if (l<=H && A[l]>A[i])large=l;
  else large=i;

  if (r<=H && A[r]>A[large])large=r;

  if(large!=i){
    temp=A[i];
    A[i]=A[large];
    A[large]=temp;
    maxheap(A,large);
  }
}
```