Make It Connected

- 给定一张无向图。 - 每次操作你可以选择一个点 $x$. - 对于所有 $y\neq x$，如果 $(x,y)$ 之间有边则删去这条边，不然加入这条边。 - 求至少需要几次操作才能使得图联通，并且构造方案。 - 多测，$\sum n\leq 4000$。

You are given a simple undirected graph consisting of $ n $ vertices. The graph doesn't contain self-loops, there is at most one edge between each pair of vertices. Your task is simple: make the graph connected. You can do the following operation any number of times (possibly zero): - Choose a vertex $ u $ arbitrarily. - For each vertex $ v $ satisfying $ v\ne u $ in the graph individually, if $ v $ is adjacent to $ u $ , remove the edge between $ u $ and $ v $ , otherwise add an edge between $ u $ and $ v $ . Find the minimum number of operations required to make the graph connected. Also, find any sequence of operations with the minimum length that makes the graph connected.

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1\leq t\leq 800 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 2\leq n\leq 4000 $ ) — the number of vertices in the graph. Then $ n $ lines follow. The $ i $ -th row contains a binary string $ s_i $ of length $ n $ , where $ s_{i,j} $ is '1' if there is an edge between vertex $ i $ and $ j $ initially, otherwise $ s_{i,j} $ is '0'. It is guaranteed that $ s_{i,i} $ is always '0' and $ s_{i,j}=s_{j,i} $ for $ 1\leq i,j\leq n $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 4000 $ .

For each test case, in the first line, output an integer $ m $ — the minimum number of operations required. If $ m $ is greater than zero, then print an extra line consisting of $ m $ integers — the vertices chosen in the operations in your solution. If there are multiple solutions with the minimum number of operations, print any.

4
3
011
100
100
3
000
001
010
4
0100
1000
0001
0010
6
001100
000011
100100
101000
010001
010010

0
1
1
2
3 4 
3
2 5 6

In the first test case, the graph is connected at the beginning, so the answer is $ 0 $ . In the second test case, if we do the operation with vertex $ 1 $ , we will get the following graph represented by an adjacency matrix: $$ \begin{bmatrix} 0&1&1\\ 1&0&1\\ 1&1&0 \end{bmatrix} $$ It's obvious that the graph above is connected. In the third test case, if we do the operation with vertex $ 3 $ and $ 4 $ , we will get the following graph represented by an adjacency matrix: $$ \begin{bmatrix} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{bmatrix} $$ It's obvious that the graph above is connected, and it can be proven that we can't perform less than $2$ operations to make the graph connected.