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 8.8.3) (judge verdict: Accepted)

import Control.Monad.State.Strict
import Data.Bool
import qualified Data.ByteString.Char8 as C
import Data.Coerce
import qualified Data.IntMap as M
import Data.Tuple
import Data.Vector.Generic ((!))
import qualified Data.Vector as V
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as U

main = sol <$> gett >>= print

gett = U.unfoldr (runStateT $ (,) <$> geti <*> geti) <$> C.getContents

geti = coerce $ C.readInt . C.dropWhile (<'0') :: StateT C.ByteString Maybe Int

sol v = pred . fst $ lowlink 0 1 M.empty
  where
  n = fst $ U.head v
  g = V.accumulate (flip (:)) (V.replicate (n+1) [])
    $ V.concatMap (V.fromList . liftM2 (:) swap return)
    $ (G.convert :: U.Vector (Int, Int) -> V.Vector (Int,Int)) $ U.tail v
  lowlink s t low = (c', low')
    where
    (c,low') = foldr f (0, M.insert t (M.size low) low) $ g!t
    c' = c + bool 0 1 (M.size low==low' M.! t)
    f i (c,low)
      | i == s          = (c,low)
      | M.member i low  = (c,M.adjust (min (low M.! i)) t low)
      | otherwise       = (c+c',M.adjust (min (low' M.! i)) t low')
      where
      (c',low') = lowlink t i low