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)

{-# LANGUAGE FlexibleContexts #-}
import Control.Applicative
import Control.Monad.ST
import Control.Monad
import Control.Monad.State
import Control.Monad.List
import Data.Array.ST
import Data.STRef
import Data.List
import Data.Tuple
import Data.Maybe
import Debug.Trace

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)
listToTuple2 [a,b] = (a,b)

bridge n edges = runST $ do
  ord <- newArray (1,n) (-1) :: ST s (STArray s Int Int)
  low <- newArray (1,n) (-1) :: ST s (STArray s Int Int)

  order <- newSTRef 0 :: ST s (STRef s Int)
  
  let
    dfs cur par order es = do
      let (connected, others) = partition ((==cur) . fst) es
      readSTRef order >>= \x -> writeArray ord cur x >> writeArray low cur x
      modifySTRef order (+1)
      
      forM_ connected $ \(_,next) -> do
        nextOrder <- readArray ord next
        when (next /= par) $ do
          if nextOrder == -1 then do
            dfs next cur order others
            readArray low next >>= \x -> modifyArray low cur (\y -> min y x)
            else
            readArray ord next >>= \x -> modifyArray low cur (\y -> min y x)

  dfs 1 (-1) order edges

  res <- forM edges $ \(u,v) -> do
    a <- readArray ord u
    b <- readArray low v
    return $ if a<b then Just (u,v) else Nothing
  return $ catMaybes res

main = do
  (n,m) <- listToTuple2 . map read . words <$> getLine :: IO (Int,Int)
  edges <- map (listToTuple2 . map read . words) . lines <$> getContents :: IO [(Int,Int)]

  print $ length $ bridge n (edges ++ (map swap edges))