### 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 $v_{i+1 \bmod n}$.

### 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.

### 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.

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.