Problem Statement

You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$-th edge connects vertex $A_i$ and vertex $B_i$. Let us delete zero or more edges to remove cycles from the graph. Find the minimum number of edges that must be deleted for this purpose.

What is a simple undirected graph? A simple undirected graph is a graph without self-loops or multi-edges whose edges have no direction.

What is a cycle? A cycle in a simple undirected graph is a sequence of vertices $(v_0, v_1, \\ldots, v_{n-1})$ of length at least $3$ satisfying $v_i \\neq v_j$ if $i \\neq j$ such that for each $0 \\leq i < n$, there is an edge between $v_i$ and $v_{i+1 \\bmod n}$.

Constraints

• $1 \\leq N \\leq 2 \\times 10^5$
• $0 \\leq M \\leq 2 \\times 10^5$
• $1 \\leq A_i, B_i \\leq N$
• The given graph is simple.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\\vdots$ $A_M$ $B_M$

Output

Print the answer.

Sample Input 1

6 7
1 2
1 3
2 3
4 2
6 5
4 6
4 5

Sample Output 1

2

One way to remove cycles from the graph is to delete the two edges between vertex $1$ and vertex $2$ and between vertex $4$ and vertex $5$.
There is no way to remove cycles from the graph by deleting one or fewer edges, so you should print $2$.

Sample Input 2

4 2
1 2
3 4

Sample Output 2

0

Sample Input 3

5 3
1 2
1 3
2 3

Sample Output 3

1