#include<iostream>
using namespace std;
#define MAX 2000000

int H, A[MAX+1];

void maxHeapify(int i){
    int l, r, largest;
    l = 2*i;
    r = 2*i+1;

    // 左の子、自分、右の子で値が最大のノードを選ぶ
    if(l<=H && A[l]>A[i]) largest = l;
    else largest = i;
    if(r<=H && A[r]>A[largest]) largest = r;

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

int main(int argc, char const *argv[])
{
    cin >> H;

    for(int i=1; i<=H; i++) cin >> A[i];

    for(int i=H/2; i>=1; i--) maxHeapify(i);

    for(int i=1; i<=H; i++){
        cout << " " <<A[i];
    }
    cout << endl;

    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<iostream>
using namespace std;
#define MAX 2000000

int H, A[MAX+1];

void maxHeapify(int i){
    int l, r, largest;
    l = 2*i;
    r = 2*i+1;

    // 左の子、自分、右の子で値が最大のノードを選ぶ
    if(l<=H && A[l]>A[i]) largest = l;
    else largest = i;
    if(r<=H && A[r]>A[largest]) largest = r;

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

int main(int argc, char const *argv[])
{
    cin >> H;

    for(int i=1; i<=H; i++) cin >> A[i];

    for(int i=H/2; i>=1; i--) maxHeapify(i);

    for(int i=1; i<=H; i++){
        cout << " " <<A[i];
    }
    cout << endl;

    return 0;
}


```