Maximum of minimum for every window size
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  Difficulty: Hard   Marks: 8
       

Given an integer array A[] of size N. The task is to find the maximum of the minimum of every window size in the array.
Note: Window size varies from 1 to n.

Input:
The first line contains an integer T denoting the total number of test cases. In each test cases, the first line contains an integer N denoting the size of array. The second line contains N space-separated integers A1, A2, ..., AN denoting the elements of the array.

Output:
In each seperate line, print the array of numbers of size N for each of the considered window size 1, 2 , ..., N respectively.

Constraints:
1 <= T <= 50
1 <= N <= 105
1 <= A[i] <= 106

Example:
Input: 
2
7
10 20 30 50 10 70 30
3
10 20 30

Output: 
70 30 20 10 10 10 10 
30 20 10

Explaination:
Testcase 1:
First element in output indicates maximum of minimums of all windows of size 1. Minimums of windows of size 1 are {10}, {20}, {30}, {50}, {10}, {70} and {30}. Maximum of these minimums is 70.
Second element in output indicates maximum of minimums of all windows of size 2. Minimums of windows of size 2 are {10}, {20}, {30}, {10}, {10}, and {30}. Maximum of these minimums is 30.
Third element in output indicates maximum of minimums of all windows of size 3. Minimums of windows of size 3 are {10}, {20}, {10}, {10} and {10}. Maximum of these minimums is 20.
Similarly other elements of output are computed.
 

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

Author: abhiraj26


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