Pinely Round 1 (Div. 1 + Div. 2) |
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Finished |
You 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:
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.
Each 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.
For 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.
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
In 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 $$$A_3$$$.
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