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 Lua (5.3.2) (judge verdict: Accepted)

local n, m = io.read("*n", "*n")
local t = {}
local as, bs = {}, {}
for i = 1, n do t[i] = {} end
for i = 1, m do
  local a, b = io.read("*n", "*n")
  as[i], bs[i] = a, b
  t[a][b], t[b][a] = true, true
end

local function check(tbl)
  local reached = {true}
  for i = 2, n do reached[i] = false end
  local reachnum = 1
  local tasks = {1}
  local tasknum, done = 1, 0
  while done < tasknum do
    done = done + 1
    local idx = tasks[done]
    for k, v in pairs(tbl[idx]) do
      if v and not reached[k] then
        table.insert(tasks, k)
        reached[k] = true
        reachnum = reachnum + 1
        tasknum = tasknum + 1
      end
    end
  end
  return n == reachnum
end
local ret = 0
for i = 1, m do
  t[as[i]][bs[i]], t[bs[i]][as[i]] = false, false
  if not check(t) then ret = ret + 1 end
  t[as[i]][bs[i]], t[bs[i]][as[i]] = true, true
end
print(ret)