#include<bits/stdc++.h>
using namespace std;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i,n) for(UL i=0; i<(n); i++)

UL N;
int A[500000];

void maxHeapify(UL i){
 UL l = (i<<1)+1;
 UL r = (i<<1)+2;
 UL largest;
 if(l<N && A[l]>A[i]) largest = l;
 else largest = i;
 if(r<N && A[r]>A[largest]) largest = r;

 if(largest != i){
  swap(A[i],A[largest]);
  maxHeapify(largest);
 }
}

void buildMaxHeap(){ for(UL i=(N-1)/2; i!=~0; i--) maxHeapify(i); }

int main() {
 scanf("%u",&N);
 rep(i,N) scanf("%d",&A[i]);
 buildMaxHeap();
 rep(i,N) printf(" %d",A[i]); printf("\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>
using namespace std;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i,n) for(UL i=0; i<(n); i++)

UL N;
int A[500000];

void maxHeapify(UL i){
 UL l = (i<<1)+1;
 UL r = (i<<1)+2;
 UL largest;
 if(l<N && A[l]>A[i]) largest = l;
 else largest = i;
 if(r<N && A[r]>A[largest]) largest = r;

 if(largest != i){
  swap(A[i],A[largest]);
  maxHeapify(largest);
 }
}

void buildMaxHeap(){ for(UL i=(N-1)/2; i!=~0; i--) maxHeapify(i); }

int main() {
 scanf("%u",&N);
 rep(i,N) scanf("%d",&A[i]);
 buildMaxHeap();
 rep(i,N) printf(" %d",A[i]); printf("\n");
 return 0;
}


```