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 A_{1}, A_{2}, ..., A_{N} 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 <= 10^{5}

1 <= A[i] <= 10^{6}

**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.

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