C. Set Constructiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a binary matrix b (all elements of the matrix are 0 or 1) of n rows and n columns.You need to construct a n sets A_1, A_2, \ldots, A_n, for which the following conditions are satisfied:  Each set is nonempty and consists of distinct integers between 1 and n inclusive.  All sets are distinct.  For all pairs (i,j) satisfying 1\leq i, j\leq n, b_{i,j}=1 if and only if A_i\subsetneq A_j. In other words, b_{i, j} is 1 if A_i is a proper subset of A_j and 0 otherwise. Set X is a proper subset of set Y, if X is a nonempty subset of Y, and X \neq Y.It's guaranteed that for all test cases in this problem, such n sets exist. Note that it doesn't mean that such n sets exist for all possible inputs.If there are multiple solutions, you can output any of them.InputEach test contains multiple test cases. The first line contains a single integer t (1\le t\le 1000) — the number of test cases. The description of test cases follows.The first line contains a single integer n (1\le n\le 100).The following n lines contain a binary matrix b, the j-th character of i-th line denotes b_{i,j}.It is guaranteed that the sum of n over all test cases does not exceed 1000.It's guaranteed that for all test cases in this problem, such n sets exist. OutputFor each test case, output n lines.For the i-th line, first output s_i (1 \le s_i \le n)  — the size of the set A_i. Then, output s_i distinct integers from 1 to n  — the elements of the set A_i.If there are multiple solutions, you can output any of them.It's guaranteed that for all test cases in this problem, such n sets exist. ExampleInput
2
4
0001
1001
0001
0000
3
011
001
000
Output
3 1 2 3
2 1 3
2 2 4
4 1 2 3 4
1 1
2 1 2
3 1 2 3
NoteIn the first test case, we have A_1 = \{1, 2, 3\}, A_2 = \{1, 3\}, A_3 = \{2, 4\}, A_4 = \{1, 2, 3, 4\}. Sets A_1, A_2, A_3 are proper subsets of A_4, and also set A_2 is a proper subset of A_1. No other set is a proper subset of any other set.In the second test case, we have A_1 = \{1\}, A_2 = \{1, 2\}, A_3 = \{1, 2, 3\}. A_1 is a proper subset of A_2 and A_3, and A_2 is a proper subset of A_3.
2
4
0001
1001
0001
0000
3
011
001
000

3 1 2 3 2 1 3 2 2 4 4 1 2 3 4 1 1 2 1 2 3 1 2 3 
['constructive algorithms', 'dfs and similar', 'graphs', 'greedy', '*1400']