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)

import math
from functools import reduce
from collections import deque
import sys
sys.setrecursionlimit(10**7)

def input():
    return sys.stdin.readline().strip()

# スペース区切りの入力を読み込んで数値リストにして返します。
def get_nums_l():
    return [ int(s) for s in input().split(" ")]

# 改行またはスペース区切りの入力をすべて読み込んでイテレータを返します。
def get_all_int():
    return map(int, open(0).read().split())

def log(*args):
    print("DEBUG:", *args, file=sys.stderr)

class union_find():
    def __init__(self, n):
        self.nodes = n
        self.node_groups = [ i for i in range(n)]
        self.group_sizes = [ 1 for _ in range(n)]
        self.group_ranks = [ 0 for _ in range(n)]

    def root(self, i):
        if self.node_groups[i] == i:
            return i
        else:
            self.node_groups[i] = self.root(self.node_groups[i])
            return self.node_groups[i]

    def same(self, a, b):
        return self.root(a) == self.root(b)

    def size(self, i):
        return self.group_sizes[self.root(i)]

    def unite(self, a, b):
        a = self.root(a)
        b = self.root(b)

        if a == b:
            return

        if self.group_ranks[a] < self.group_ranks[b]:
            self.group_sizes[b] += self.size(a)
            self.node_groups[a] = b
        else:
            self.group_sizes[a] += self.size(b)
            self.node_groups[b] = a
            if self.group_ranks[a] == self.group_ranks[b]:
                self.group_ranks[a] += 1


def main():
    INF = 999999999999999999999999
    MOD = 10**9+7

    n,m = get_nums_l()

    uf = union_find(n)

    for i in range(m):
        a,b = get_nums_l()
        a-=1
        b-=1
        uf.unite(a,b)
    
    groups = len(set([ uf.root(i) for i in range(n) ]))

    print(groups-1)

main()