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: Wrong Answer)

N, M = map(int, input().split(" "))

doubled = set()
s = set()

bridges = {}
conditions = {}
cs = set(range(M)) # conditionのセット
for i in range(M):
    a, b = map(int, input().split(" "))
    for j in range(a - 1, b -1):
        idx = "{}".format(j)
        bridges[idx] = bridges.get(idx, 0) + 1
        conditions.setdefault(idx, []).append(i)
bridges = sorted(bridges.items(), key=lambda x: x[1], reverse=True)

num_break = 0
for b, j in bridges:
    if len(cs) == 0:
        break
    flag = False
    for i in conditions[b]:
        if i in cs:
            flag = True
            cs.remove(i)
    if flag:
        num_break += 1

print(num_break)