There are $$$N$$$ persons. Each one of them has a friendship with zero or more of others. If $$$A$$$ is friend with $$$B$$$, then $$$B$$$ is also friend with $$$A$$$. Now they will have to form some teams, each containing two persons. Each member of a team must have a friendship with the other member of the team. The question is, what is the maximum number of teams that can be made?

For example,
$$$A$$$ is friend with $$$B$$$ and $$$D$$$.
$$$B$$$ is friend with $$$A$$$ and $$$C$$$.
$$$C$$$ is friend with $$$B$$$.
$$$D$$$ is friend with $$$A$$$.

Then, maximum two teams can be made:

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How to solve this if,

• the upper bound of $$$N$$$ is $$$100$$$?
• the upper bound of $$$N$$$ is $$$1000$$$?
• the number of team members is any number in the range $$$[2,N]$$$?