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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

module union_find_mod
    use,intrinsic :: iso_fortran_env
    private
    type,public:: union_find
        integer(int32),allocatable:: parent(:)
    contains
        procedure:: unite => uf_unite
        procedure:: root => uf_root
    end type

    interface union_find
        module procedure:: uf_init
    end interface
contains
    function uf_init(n) result(uf)
        type(union_find):: uf
        integer(int32):: n
        allocate(uf%parent, source=[(i,i=1,n)])
    end function


    function uf_root(uf,x) result(ret)
        class(union_find):: uf
        integer(int32):: x,ret

        ret = x
        do while(ret /= uf%parent(ret))
            ret = uf%parent(ret)
        end do
    end function


    subroutine uf_unite(uf,a,b)
        class(union_find):: uf
        integer(int32),intent(in):: a,b
        integer(int32):: ra, rb

        ra = uf%root(a); rb = uf%root(b)
        if (ra == rb) return
        uf%parent(ra) = rb
    end subroutine
end module


program main
    use,intrinsic :: iso_fortran_env
    use union_find_mod
    implicit none
    integer(int32):: n,m,i,a,b,ans
    type(union_find):: uf
    integer(int32), allocatable:: cnt(:)


    read*, n,m
    uf = union_find(n)
    allocate(cnt(n),source=0)

    do i=1,m
        read*, a,b
        call uf%unite(a,b)
    end do

    do i=1,n
        cnt(uf%root(i)) = cnt(uf%root(i)) + 1
    end do
    ans=0
    do i=1,n
        if (cnt(i) > 0) ans=ans+1
    end do
    print'(i0)',ans-1
end program main