Problem:
Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

class UnionFind():
    def __init__(self,n):
        self.n = n
        self.parents = [-1] * n

    # 根を返す
    def find(self,x):
        if self.parents[x]<0:
            return x
        else:
            self.parents[x]=self.find(self.parents[x])
            return self.parents[x]

    # 合併する
    def union(self,x,y):
        x=self.find(x)
        y=self.find(y)

        if x==y:
            return

        if self.parents[x] > self.parents[y]:
            x,y=y,x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    # 同じグループに属するかを判定する
    def same(self,x,y):
        return self.find(x)==self.find(y)

    # 属するグループの要素数を判定する
    def size(self,x):
        return self.parents[self.find(x)]*(-1)

    # 属するグループの要素を返す
    def members(self,x):
        root=self.find(x)
        return [i for i in range(self.n) if self.find(i)==root]

    # すべての根の要素を返す
    def root(self):
        return [i for i,x in enumerate(self.parents) if x<0]

    # グループの数を返す
    def group_count(self):
        return len(self.root())

    # ｛根：その要素｝の辞書を返す
    def all_group_members(self):
        return {r: self.members(r) for r in self.root()}

    # ｛根：その要素｝で表示する
    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

N,M=map(int,input().split())
UF=UnionFind(N)

for i in range(M):
    x,y=map(int,input().split())
    x,y=x-1,y-1
    UF.union(x,y)

ans=UF.group_count()-1
print(ans)