Problem Statement

There is a simple connected undirected graph with $N$ vertices and $M$ edges. The edges are numbered from $1$ to $M$, and edge number $i\ (1\le i \le M)$ connects vertices $u_i,\ v_i$.

chinerist performed the following operation repeatedly until the graph had no edges left.

• For each connected component of the graph, if the connected component has edges, delete the edge with the smallest edge number in it.

Find how many times chinerist performed the operation (even if multiple edges are deleted during an operation, it counts as $1$ operation).

Input

$N$ $M$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_M$ $v_M$

• $2 \leq N \leq 2 \times 10^5$
• $N-1 \leq M \leq \min(\frac{N(N-1)}{2},\ 2\times 10^5)$
• $1 \leq u_i < v_i \leq N$
• The input consists of integers.
• The given graph is a simple connected undirected graph.

Output

Output the answer.

Print a newline at the end.

Sample

4 3
2 3
1 2
3 4

2

12 20
6 8
1 5
3 5
2 9
2 11
11 12
5 9
7 12
4 11
5 8
7 10
7 11
1 7
7 8
7 9
4 10
6 12
8 11
2 3
1 12

15