#include<bits/stdc++.h>
//#define pb push_back
using namespace std;
int h,x;
int a[1000002];
void maxheap(int i){
	 int l=2*i,t,m=i;
	 if (a[l]>a[i] && l<=h)
	    m=l;
	 if (a[l+1]>a[m] && (l+1)<=h)
        m=l+1;
     if (m!=i){
     	t=a[i]; a[i]=a[m]; a[m]=t;
	    maxheap(m);
	 }
	 	   
}
int main(){
	cin>>h;
	//a.pb(0);
	for (int i=1; i<=h; i++){
		cin>>a[i];
	} 
	for (int i=h/2; i>=1; i--)
	    maxheap(i);
	for (int i=1; i<=h; i++)
	    cout<<' '<<a[i];
    cout<<'\n';
    return 0;
}

### Prompt

Create a solution in cpp for 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<bits/stdc++.h>
//#define pb push_back
using namespace std;
int h,x;
int a[1000002];
void maxheap(int i){
	 int l=2*i,t,m=i;
	 if (a[l]>a[i] && l<=h)
	    m=l;
	 if (a[l+1]>a[m] && (l+1)<=h)
        m=l+1;
     if (m!=i){
     	t=a[i]; a[i]=a[m]; a[m]=t;
	    maxheap(m);
	 }
	 	   
}
int main(){
	cin>>h;
	//a.pb(0);
	for (int i=1; i<=h; i++){
		cin>>a[i];
	} 
	for (int i=h/2; i>=1; i--)
	    maxheap(i);
	for (int i=1; i<=h; i++)
	    cout<<' '<<a[i];
    cout<<'\n';
    return 0;
}

```