The task is to complete heapify() and buildHeap() functions which are used to implement Heap Sort. 

Input:
First line of the input denotes number of test cases 'T'. First line of the test case is the size of array and second line consists of array elements.

Output:
Sorted array in ascending order.

Constraints:
1 <=T<= 50
1 <=N<= 1000
1 <=arr[i]<= 1000

Example:

Input:
2
5
4 1 3 9 7
10
10 9 8 7 6 5 4 3 2 1

Output:
1 3 4 7 9
1 2 3 4 5 6 7 8 9 10

Note:The Input/Ouput format and Example given below is used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console, and should not print anything on stdout/console. The task is to complete the function specified, and not to write the full code.

** For More Input/Output Examples Use 'Expected Output' option **