B. Array
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an integer array $$$a$$$ of length $$$n$$$.

For each index $$$i$$$, find the maximum number of indices $$$j$$$ such that $$$j \gt i$$$ and $$$|a_i - k| \gt |a_j - k|$$$, over all possible integer values of $$$k$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 5000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5000$$$.

Output

For each test case, output $$$n$$$ integers denoting the answer.

Example
Input
6
1
1092
2
105 -105
5
1 2 93 84 2
7
2 9 38 4 7 1 6
10
1 9 20 9 829 3 87 1 283 7
11
9 18 29817 283 3 3928 5726 1942 1000000000 -1000000000 19
Output
0
1 0
4 2 2 1 0
5 4 4 2 2 1 0
8 4 4 3 5 3 2 2 1 0
8 7 7 4 5 3 3 2 2 1 0
Note

In the second test, the answers are:

  • For $$$i=1$$$, you can choose $$$k=-195$$$, then $$$j=2$$$.
  • For $$$i=2$$$, you can choose $$$k=5$$$, there exists no index $$$j \gt i$$$.

In the third test, the answers are:

  • For $$$i=1$$$, you can choose $$$k=195$$$, then $$$j=2,3,4,5$$$.
  • For $$$i=2$$$, you can choose $$$k=78$$$, then $$$j=3,4$$$.
  • For $$$i=3$$$, you can choose $$$k=15$$$, then $$$j=4,5$$$.
  • For $$$i=4$$$, you can choose $$$k=15$$$, then $$$j=5$$$.
  • For $$$i=5$$$, you can choose $$$k=998\,244\,353$$$, there exists no index $$$j \gt i$$$.