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Min Max Riddle

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Given an integer array of size , find the maximum of the minimum(s) of every window size in the array. The window size varies from to .

For example, given , consider window sizes of through . Windows of size are . The maximum value of the minimum values of these windows is . Windows of size are and their minima are . The maximum of these values is . Continue this process through window size to finally consider the entire array. All of the answers are .

Function Description

Complete the riddle function in the editor below. It must return an array of integers representing the maximum minimum value for each window size from to .

riddle has the following parameter(s):

  • arr: an array of integers

Input Format

The first line contains a single integer, , the size of .
The second line contains space-separated integers, each an .

Constraints

Output Format

Single line containing space-separated integers denoting the output for each window size from to .

Sample Input 0

4
2 6 1 12

Sample Output 0

12 2 1 1

Explanation 0

Here and

window size window1 window2 window3 window4 maximum of all windows
1 2 6 1 12 12
2 2 1 1 2
3 1 1 1
4 1 1

Sample Input 1

7
1 2 3 5 1 13 3

Sample Output 1

13 3 2 1 1 1 1

Explanation 1

Here and

win size w_1 w_2 w_3 w_4 w_5 w_6 w_7 maximum of all windows
1 1 2 3 5 1 13 3 13
2 1 2 3 1 1 3 3
3 1 2 1 1 1 2
4 1 1 1 1 1
5 1 1 1 1
6 1 1 1
7 1 1

Sample Input 2

6
3 5 4 7 6 2

Sample Output 2

7 6 4 4 3 2

Explanation 2

Here and

win size w_1 w_2 w_3 w_4 w_5 w_6 maximum of all windows
1 3 5 4 7 6 2 7
2 3 4 4 6 2 6
3 3 4 4 2 4
4 3 4 2 4
5 3 2 3
6 2 2
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