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