Friend Groups

There are n people, numbered 0 to n - 1, and a list of friendships pairs, where [a, b] means a and b are friends. Friends of friends end up in the same group: if Ana is friends with Ben and Ben is friends with Cy, all three are in one group, even if Ana and Cy have never met. Write count_groups(n, pairs) that returns the number of groups.

A person with no friends forms a group of one.

Examples

count_groups(5, [[0, 1], [1, 2], [3, 4]])  # returns 2
count_groups(4, [])  # returns 4
count_groups(3, [[0, 1], [1, 2], [2, 0]])  # returns 1

In the first example people 0, 1 and 2 form one group and people 3 and 4 form another.

Constraints

• 0 <= n <= 2000, with up to 5,000 pairs.
• The two people in a pair are different, and a pair may be listed more than once, in either order.