Illness#6284
In Byteland, an epidemic of a dangerous disease has broken out. It is known that the disease is caused by different pathogenic bacteria.
To correctly treat a patient, doctors need to know which specific bacteria caused the illness. For this purpose, the patient undergoes tests: each test checks for the presence or absence of certain types of bacteria. A test returns a positive result if at least one of the bacteria types it checks for is present in the person's blood.
Help the doctors determine, based on the test results, whether the patient is infected with each bacterium.
The first line contains two integers (1 \leq n \leq 100) — the number of different disease pathogens, and (1 \leq m \leq 10000) — the number of tests. Each of the next lines contains n + 1 integers. The first integers describe which pathogens are checked by this test: the -th number is if the test checks for the -th pathogen, and otherwise.
The last number in the line is if the test returned a positive result, and otherwise.
If the data is contradictory, output a single line: Incorrect. Otherwise, output three lines. Each line must be in the format: the number of bacteria, followed by their indices.
On the first line, print the indices of bacteria that definitely cannot be the cause of the disease. On the second line, print the indices of bacteria that are known to be the cause of the disease. On the third line, print the indices of bacteria for which nothing can be determined based on the test results.
Example 1