Problem Statement

In the coordinate plane, we have 2N vertices whose x-coordinates are $1, 2, \ldots, N$ and whose y-coordinates are 0 or 1: $(1, 0),\ldots, (N,0), (1,1), \ldots, (N,1)$.
There are M segments that connect two of these vertices: the i-th segment connects (a_i, 0) and (b_i, 1).
Consider choosing K of these M segments so that no two chosen segments contain the same point. Here, we consider both endpoints of a segment to be contained in that segment. Find the maximum possible value of K.

Input

Input is given from Standard Input in the following format:
N M
a_1 b_1
$\vdots$
a_M b_M

Output

Print the maximum possible value of K.

Constraints

• $1\leq N, M \leq 2\times 10^5$
• $1\leq a_i, b_i\leq N$
• $a_i\neq a_j$ or $b_i\neq b_j$, if $i\neq j$.

Sample Input 1

3 3
1 2
2 3
3 1

Sample Output 1

2

One optimal solution is to choose the first and second segments.
The first and third segments, for example, contain the same point $\left(\frac53, \frac23\right)$, so we cannot choose them both.

Sample Input 2

3 5
1 1
2 1
2 2
3 2
3 3

Sample Output 2

3

One optimal solution is to choose the first, third, and fifth segments.
The first and second segments, for example, contain the same point (1, 1), so we cannot choose them both.

Sample Input 3

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

Sample Output 3

1

见题面 Input 部分

见题面 Output 部分