Problem:
Score : 300 points

Problem Statement

You are given an undirected connected graph with N vertices and M edges that does not contain self-loops and double edges.

The i-th edge (1 \leq i \leq M) connects Vertex a_i and Vertex b_i.

An edge whose removal disconnects the graph is called a bridge.

Find the number of the edges that are bridges among the M edges.

Notes

A self-loop is an edge i such that a_i=b_i (1 \leq i \leq M).

Double edges are a pair of edges i,j such that a_i=a_j and b_i=b_j (1 \leq i<j \leq M).

An undirected graph is said to be connected when there exists a path between every pair of vertices.

Constraints

2 \leq N \leq 50

N-1 \leq M \leq min(N(N−1)⁄2,50)

1 \leq a_i<b_i \leq N

The given graph does not contain self-loops and double edges.

The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the edges that are bridges among the M edges.

Sample Input 1

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 1

4

The figure below shows the given graph:

The edges shown in red are bridges. There are four of them.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

0

It is possible that there is no bridge.

Sample Input 3

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 3

5

It is possible that every edge is a bridge.

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

module UnionFind
implicit none
integer,allocatable,dimension(:)::par
!parentより

contains
subroutine UFinit(N)
  integer :: N,i
  allocate(par(N))
    do i = 1, N
      par(i) = i
    end do
  end subroutine
  recursive function root(x) result (res)
    integer :: x, res
    if (par(x) == x)then
       res = x
    else
      res = root(par(x))
      par(x) = res
    end if
  end function

subroutine unite(x,y)
integer,intent(in):: x,y
integer xr,yr
xr = root(x)
yr = root(y)
if(xr /= yr) par(xr) = yr
end subroutine

end module UnionFind

use UnionFind
integer N,M
integer,allocatable,dimension(:)::a,b
integer ans,cnt
integer i,j
read*,N,M
allocate(A(M),B(M))
do i=1,M
  read*,A(i),B(i)
end do

ans=0
do i=1,M
  call UFinit(N)
  do j=1,M
    if(i==j)cycle
    call unite(a(j),b(j))
  end do
  cnt=0
  do j=1,N
    if(root(j)==j)cnt=cnt+1
  end do
  if(cnt>=2)then
    ans=ans+1
  endif
  deallocate(par)
end do
print"(i0)",ans
end