Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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.

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.

Constraint

$1 \leq H \leq 500,000$

$-2,000,000,000 \leq$ value of a node $\leq 2,000,000,000$

Sample Input 1

10
4 1 3 2 16 9 10 14 8 7

Sample Output 1

16 14 10 8 7 9 3 2 4 1

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JavaScript (judge verdict: Accepted)

var h,n;

function maxHeapify(i){
    var l = i * 2;
    var r = i * 2 + 1;

    var largest;
    if(l <= n && h[l] > h[i]){
        largest = l;
    }
    else
        largest = i;
    if(r <= n  && h[r] > h[largest])
        largest = r;

    if(largest != i){
        var ex;
        ex = h[i];
        h[i] = h[largest];
        h[largest] = ex;
        maxHeapify(largest);
    }
}

function buildMaxHeap(){
    for(var i = n/*Math.floor((n + 1) / 2)*/;i >= 1;i--)
        maxHeapify(i);
}

function Main(input){
    input = input.split("\n");
    n = parseInt(input[0],10);
    input[1] = input[1].split(" ");
    h = new Array(n + 1);
    for(var i = 1;i <= n;i++)
        h[i] = parseInt(input[1][i - 1],10);

    buildMaxHeap();

    for(var i = 1;i <= n;i++){
        String(h[i]);
    }

    var ans = "";

    for(var i = 1;i <= n;i++){
        ans += " " + h[i];
    }
    console.log(ans);
    
}
 
Main(require("fs").readFileSync("/dev/stdin","utf8"));