class DisjointSet:
    def __init__(self, vertices):
        vertices = list(vertices)
        if len(set(vertices)) != len(vertices):
            raise ValueError("Repeated vertex")
        self.parent = {vertex: vertex for vertex in vertices}
        self.size = {vertex: 1 for vertex in vertices}
        self.components = len(vertices)

    def find(self, vertex):
        if vertex not in self.parent:
            raise ValueError("Unknown vertex")
        while self.parent[vertex] != vertex:
            self.parent[vertex] = self.parent[self.parent[vertex]]
            vertex = self.parent[vertex]
        return vertex

    def union(self, first, second):
        first, second = self.find(first), self.find(second)
        if first == second:
            return False
        if self.size[first] < self.size[second]:
            first, second = second, first
        self.parent[second] = first
        self.size[first] += self.size[second]
        self.components -= 1
        return True

groups = DisjointSet(["gate", "oak", "pond"])
print(groups.union("gate", "oak"))
print(groups.union("oak", "gate"))
print(groups.components)
print(groups.find("gate") == groups.find("oak"))