human
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.

Example

Input

10
4 1 3 2 16 9 10 14 8 7

Output

16 14 10 8 7 9 3 2 4 1
Solve the task in PYTHON3.
assistant
#Here is Python code to print values of nodes in the max-heap in order of their id (from $1$ to $H$).

class MaxHeap:
    def __init__(self):
        self.heap = []
        self.length = 0

    def __str__(self):
        return " " + " ".join(str(n) for n in self.heap)

    def up_insert(self, key):
        self.heap.append(key)
        self._upheap()
        self.length += 1

    def down_insert(self, key):
        self.heap.append(key)
        self.length += 1
        for i in range(self.length // 2, -1, -1):
            self._downheap(i)

    def down_many_insert(self, key):
        self.heap.extend(key)
        self.length += len(key)
        for i in range(self.length // 2, -1, -1):
            self._downheap(i)

    def _upheap(self):
        index = self.length - 1
        while True:
            parent_index = (index - 1) // 2
            if parent_index < 0 or self.heap[parent_index] >= self.heap[index]:
                break
            self.heap[parent_index], self.heap[index] = self.heap[index], self.heap[parent_index]
            index = parent_index

    def _downheap(self, index):
        while True:
            child_index_left, child_index_right = index * 2 + 1, index * 2 + 2
            # print(index, child_index_left, child_index_right)
            if child_index_left >= self.length:
                break
            elif (child_index_right >= self.length or self.heap[child_index_left] > self.heap[child_index_right]) and self.heap[index] < self.heap[child_index_left]:
                self.heap[index], self.heap[child_index_left] = self.heap[child_index_left], self.heap[index]
                index = child_index_left
            elif (child_index_right < self.length and self.heap[child_index_left] < self.heap[child_index_right]) and self.heap[index] < self.heap[child_index_right]:
                self.heap[index], self.heap[child_index_right] = self.heap[child_index_right], self.heap[index]
                index = child_index_right
            else:
                break


a = MaxHeap()
length = int(input())
t = [int(n) for n in input().split(" ")]
a.down_many_insert(t)
print(a)