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 (3.8.2) (judge verdict: Wrong Answer)

# 初期入力
import sys
input = sys.stdin.readline  #文字列では使わない

N,M = map(int, input().split())
ans =0
x =set(range(1,N))
used =[]
for _ in range(M):
    a,b = map(int, input().split()) #争いのある部分
    # 争いのある部分の積集合⇒壊すべきところ
    ab_set =set(range(a,b))
    if x & ab_set:
        x =x & ab_set

    #共通部分がなかったら壊すべきところが増える
    else:
        for u in used:
            if u & ab_set:
                x = u & ab_set
                continue
        used.append(x)
        ans +=1
        x =ab_set
print(ans +1)