Find the minimum number of squads that you can

send to battle meeting the given constraints.

Background

You are assembling a Rebel Army to fight against

the Galactic Empire. For this you have invited

people from several influential families to join your

army. You want to create squads that can be sent

to battle the Empire. However you find that as

soon as you add a person with their

child, grandchild or any descendant in the same

squad they begin to give orders to the descendant

and the squad quickly falls apart. Your goal is to

find the minimum number of such squads that

you can create which do not have this problem.

In your army, each person has a maximum of

$1$ parent. A person may have one or more

ancestors that may be direct or indirect. $x$ is an

ancestor of $Y$ if at least one of the following is true:

$x$ is a parent of $Y($direct ancestor$)$

If $x$ is a parent of $Z,$ and $Z$ is a parent of $Y,$

then $x$ is an indirect ancestor of $Y.$ Indirect

ancestor is transitive through any number of

levels.

No two people will ever be mutual ancestors, and

no person is a parent of themselves. Determine

the minimum number of squads that must be

formed so that no person is in the same