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.

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

-----Sample Input-----
7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

-----Sample Output-----
4

The figure below shows the given graph:
The edges shown in red are bridges. There are four of them.

见题面

见题面