You are given a set of (n) quadratic functions (F=\{f_1,f_2,\ldots,f_n \}), where (f_i(x)=a_i x^2 + b_i x + c_i). Two functions (f) and (g) are called independent if (f(x) \neq g(x)) for all (x \in \mathbb{R}). Also, a set of functions (G=\{g_1,g_2,\ldots,g_k\}) is called organized if the two functions (g_i) and (g_j) are independent for all (1 \le i \lt j \le |G|). For each (i=1,2,\ldots,n), please find the size of the largest organized subset of (F) that contains (f_i) as an element. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 3000)). Each of the (n) following lines contains three integers (a_i), (b_i), (c_i) denoting the function (f_i) ((-10^6 \le a_i, b_i, c_i \le 10^6), (a_i \neq 0)). It is guaranteed that the functions in one test case are pairwise distinct. It is guaranteed that the sum of (n^2) over all test cases does not exceed (3000^2). For each test case, output (n) integers (s_1,s_2,\ldots,s_n), where (s_i) is the size of the largest organized subset that contains (f_i). In the first test case, the functions are as follows: (f_1(x)=x^2+2x-1); (f_2(x)=-3x^2-3); (f_3(x)=-x^2+4x-5); (f_4(x)=x^2+2x-4). The functions' graphs are as shown below: The largest organized subsets of (F) containing each function are as follows: (\{f_1,f_3,f_4\}) is the largest organized subset that contains (f_1); (\{f_1,f_2\}) is the largest organized subset that contains (f_2); (\{f_1,f_3,f_4\}) is the largest organized subset that contains (f_3); (\{f_1,f_3,f_4\}) is the largest organized subset that contains (f_4).