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: Runtime Error)

import numpy as np

n,m = map(int,input().split())
a = np.zeros(m)
b = np.zeros(m)
for k in range(m):
    a[k], b[k] = map(int,input().split())

c = np.vstack([a,b]).T.astype(np.int32)

cand = np.zeros([m,n-1])
for k in range(m):
    cand[k,c[k,0] - 1 : c[k,1] - 1] = 1

temp = np.sum(cand,axis=1) != 1
k = np.sum(np.sum(cand,axis=1) == 1)
cand = cand[temp,:]

def aaa(cand):
    a = np.argmax(np.sum(cand,axis=0))
    cand = cand[cand[:,a] == 0]
    return cand,a

while True:
    if len(cand) == 0:
        break
    cand,a = aaa(cand)
    k += 1
print(k)