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.

Note

• 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.