You are given an undirected graph with (n) vertices, labeled from (1) to (n). This graph encodes a hidden permutation(^{\text{∗}}) (p) of size (n). The graph is constructed as follows: For every pair of integers (1 \le i < j \le n), an undirected edge is added between vertex (p_i) and vertex (p_j) if and only if (p_i < p_j). Note that the edge is not added between vertices (i) and (j), but between the vertices of their respective elements. Refer to the notes section for better understanding. Your task is to reconstruct and output the permutation (p). It can be proven that permutation (p) can be uniquely determined. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 500)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 1000)). The (i)-th of the next (n) lines contains a string of (n) characters (g_{i, 1}g_{i, 2}\ldots g_{i, n}) ((g_{i, j} = \mathtt{0}) or (g_{i, j} = \mathtt{1})) — the adjacency matrix. (g_{i, j} = \mathtt{1}) if and only if there is an edge between vertex (i) and vertex (j). It is guaranteed that there exists a permutation (p) which generates the given graph. It is also guaranteed that the graph is undirected and has no self-loops, meaning (g_{i, j} = g_{j, i}) and (g_{i, i} = \mathtt{0}). It is guaranteed that the sum of (n) over all test cases does not exceed (1000). For each test case, output (n) integers $$$p_1, p_2, \ldots,