Virology

Little is understood about the virus and the way it infects its human hosts, but what has been discovered is a peculiar pattern in human DNA that can tell virologists if a particular person is vulnerable or immune to the virus. DNA was sampled from every individual working with the CDC, and a pattern was recognized to be present in only those who were infected by the virus.

We have isolated $9$ genes within human DNA that can tell us if a person is vulnerable to infection. Most people have at least $14$ occurrences of these genes. An individual that is considered vulnerable is known to have met the following conditions:

• The individual must have exactly $14$ occurrences of the numbered DNA genes ($1$-$9$). You will only test samples from people that meet this condition. There will be a max of $3$ of the same gene in a test case. The order of the genes is not significant.

• Within their DNA there must be 4 total instances of triples and/or straights and $1$ pair

• triples ($3$ of the same gene, example: [7 7 7])

• straights of $3$ (examples: [1 2 3] [7 8 9] [4 5 6])

• pair ($2$ of the same gene, example: [9 9])

Note: An instance of a gene cannot be reused in multiple sets

So if an individual with $14$ numbered genes in their DNA has

• $4$ triples/straights AND

• $1$ pair

then they are vulnerable. If this pattern cannot be found in an individual's DNA then that individual is immune.

Your job is to take a list of DNA samples from individuals with $14$ of the numbered genes and determine if they are vulnerable.