Read problem statements in [Russian], [Bengali], and [Mandarin Chinese] as well.

There are $N$ students standing in a canteen queue, numbered $1$ to $N$ from left to right. For each valid $i$, the $i$-th student has a height $h_{i}$.

Two students $i$ and $j$ can see each other if there are no taller students standing between them. Formally, students $i$ and $j$ ($i < j$) can see each other if for each integer $k$ ($i < k < j$), $h_{k} ≤ h_{i}, h_{j}$.

For each valid $i$, determine the number $c_{i}$ of students that have the same height as student $i$ and can be seen by student $i$.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $h_{1}, h_{2}, \ldots, h_{N}$.

------ Output ------
For each test case, print a single line containing $N$ space-separated integers $c_{1}, c_{2}, \ldots, c_{N}$.

------ Constraints ------
$1 ≤ T ≤ 10$
$1 ≤ N ≤ 10^{5}$
$1 ≤ h_{i} ≤ 10^{9}$ for each valid $i$
the sum of $N$ over all test cases does not exceed $10^{5}$

------ Subtasks ------
Subtask #1 (30 points): the sum of $N$ over all test cases does not exceed $10^{3}$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------
1

5

1 2 2 3 2
----- Sample Output 1 ------
0 1 1 0 0
----- explanation 1 ------
Example case 1: Student $3$ can see students $2$ and $4$, but only student $2$ has the same height (height $2$). On the other hand, student $3$ cannot see student $5$ since student $4$ is taller and therefore blocking the view.

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