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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
import Data.Array.IO
import Control.Monad

type Vertex = (Int, [Int])

main = do
  [n, m] <- map read . words <$> getLine :: IO [Int]
  edge <- (\[x, y] -> zip x y) . transpose . map (map read . words) . lines <$> getContents :: IO [(Int, Int)]
  let v = [(i, []) | i <- [1..n]]
  print =<< foldM (solve n v edge) 0 edge

makeMark :: Int -> IO (IOUArray Int Bool)
makeMark n = newArray (1, n) False

makeGraph :: [Vertex] -> (Int, Int) -> [Vertex]
makeGraph v (i, j) = write i j $ write j i v

write :: Int -> Int -> [Vertex] -> [Vertex]
write x y v = take (x-1) v ++ [(x, y:(snd $ v !! (x-1)))] ++ drop x v

search :: [Vertex] -> IOUArray Int Bool -> Int -> IO (IOUArray Int Bool)
search [] mark i = return mark
search graph mark i = do
  let (v, neighbors) = graph !! (i - 1)
  b <- readArray mark i
  case b of
    True -> do
      return mark
    False -> do
      writeArray mark i True
      return =<< foldM (search graph) mark neighbors

solve :: Int -> [Vertex] -> [(Int, Int)] -> Int -> (Int, Int) -> IO Int
solve n v edges brigde e = do
  let graph = foldl makeGraph v $ delete e edges
  mark <- makeMark n
  search graph mark 1
  ans <- and <$> getElems mark
  return $ if ans then brigde else brigde + 1