Migrated from Lutece 781 Virology

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Description

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 $\textbf{immune}$.

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

Input

The first number will be the number of test cases $N (1 \leq N \leq 200000)$. Following that will be $N$ lines of $14$ numbers separated by spaces indicating the genes present in the DNA.

Output

If an individual is vulnerable to the virus, output Vulnerable. Otherwise, output Immune. Output each answer on a separate line.

Samples

2
1 1 2 3 4 4 4 5 6 7 7 8 9 1
1 1 1 2 3 4 4 4 5 6 6 7 8 9

Vulnerable
Immune

Resources

2013 ACM ICPC South Central USA Regional Programming Contest