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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
import copy
import numpy as np


def main():
    n, m = [int(x) for x in input().split()]
    path = set([tuple([a, b]) for a in range(1, n + 1) for b in range(a + 1, n + 1)])
    war = sorted([tuple(int(e) for e in input().split()) for _ in range(m)], key=lambda x: x[1] - x[0])
    ans = 0
    for w in war:
        if w in path:
            ans += 1
            pathnext = copy.deepcopy(path)
            for p in path:
                if p[0] <= w[0] < p[1] or p[0] < w[1] <= p[1]:
                    pathnext.remove(p)
            path = pathnext
    print(ans)


main()