Description

Einstein has started learning to draw.

He is rather lazy, and he hopes to draw a picture using as few strokes as possible.

Given an undirected graph with $n$ vertices (numbered $1 \sim n$) and $m$ edges, find the minimum number of strokes needed to draw all the edges in the graph.

Input Format

The first line contains two integers $n, m$.

Each of the next $m$ lines contains two integers $a, b$ ($a \ne b$), indicating that there is an edge between vertices $a$ and $b$.

No edge is described more than once.

Output Format

A single integer, i.e., the answer.

5 5
2 3
2 4
2 5
3 4
4 5

1

Hint

For $50\%$ of the testdata, $n \le 50$, $m \le 100$.

For $100\%$ of the testdata, $1 \le n \le 1000$, $1 \le m \le {10}^5$.

Translated by ChatGPT 5