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: Time Limit Exceeded)

n, m = map(int, input().split())
list_ab = []
for _ in range(m):
    ab = list(map(int, input().split()))
    list_ab.append(ab)

total = n-1
for bit in range(2**(n-1)):
    bridge = [0] * (n-1)
    ok = True
    for i in range(n-1):
        if (bit >> i) & 1 == 1:
            bridge[i] = 1
    for j in range(m):
        if 1 not in bridge[list_ab[j][0]-1:list_ab[j][1]-1]:
            ok = False
            break
        else:
            
            pass
    if ok:
        total = min(total, sum(bridge))

print(total)