Problem:
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.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

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

Sample Input 2

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

Sample Output 2

2

Sample Input 3

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

Sample Output 3

4

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
    N, M = [int(n) for n in input().split()]
    paths = [[int(n) for n in input().split()] for _ in range(M)]
    paths.sort(key = lambda x: x[0])

    prev = (-1, -1)
    result = 0
    for l, r in paths:
        r = r - 1
        pl, pr = prev
        if pl <= l and r <= pr:
            prev = (l, r)
            continue
        elif pl <= l <= pr and pr < r:
            prev = (l, pr)
            continue
        elif pr < l :
            prev = (l, r)
            result += 1
            continue
        else:
            raise ValueError("aaa")
    print(result)
if __name__ == "__main__":
    main()