Given an array of integers $A$ of size $N$. 
You can perform the following operation on the array:

• Choose an index $i$ and remove the $i^{th}$ element from $A$.

For each, $i$ (from $1$ to $N$), output the minimum number of operations such that the integer $i$ becomes greater than BOTH of its neighbours i.e. $(A[i] > A[i-1] \ \ \&\& \ \ A[i] > A[i+1])$.

If it is not possible to satisfy the mentioned condition output $-1$ for that index

Input Format :

The first line contains $T$, the number of test cases 

The first line of all test cases contains $N$, the number of elements in the array 

The second line contains $N$ space-separated integers 

Note :  The sum of $N$ over all test cases does not exceed $10^5$

Output Format :

For every test case, output $N$ integers, where the $i^{th}$ integer represents the minimum number of moves to make the $i^{th}$ index good

Constraints:

$1 \leq T \leq 100 \\ 1 \leq N \leq 10^5 \\ 1 \leq A[i] \leq 10^9 \\$