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)

N, M = list(map(int, input().split(' ')))
edges = []
for i in range(M):
    a, b = list(map(int, input().split(' ')))
    edges.append([v for v in range(a, b)])

ans = 0
while any(edges):
    hit_index = 0
    max_hit = 0
    for v in range(N):
        hit = 0
        for i in range(M):
            if edges[i] and v in edges[i]:
                hit += 1
            if hit > max_hit:
                max_hit = hit
                hit_index = v
    # print('max_hit')
    # print(max_hit)
    # print('cut here')
    # print(hit_index)
    for i in range(len(edges)):
        if edges[i] and hit_index in edges[i]:
            edges[i] = False
    ans += 1
    # print('cutted')
    # print(edges)
print(ans)