D - Islands War

Score : $400$ points

Problem Statement

There are $N$ islands lining up from west to east, connected by $N-1$ bridges.

The $i$-th bridge connects the $i$-th island from the west and the $(i+1)$-th island from the west.

One day, disputes took place between some islands, and there were $M$ requests from the inhabitants of the islands:

Request $i$: A dispute took place between the $a_i$-th island from the west and the $b_i$-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these $M$ requests.

Find the minimum number of bridges that must be removed.

Constraints

• All values in input are integers.
• $2 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• $1 \leq a_i < b_i \leq N$
• All pairs $(a_i, b_i)$ are distinct.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$a_1$ $b_1$

$a_2$ $b_2$

$:$

$a_M$ $b_M$

Output

Print the minimum number of bridges that must be removed.

5 2
1 4
2 5

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

9 5
1 8
2 7
3 5
4 6
7 9

2

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

4