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)

import numpy as np
import copy
N,M = (int(i) for i in input().split()) 
a_tmp = [[int(i) for i in input().split()] for i in range(M)] 
a = copy.deepcopy(a_tmp)
cnt = 0
def cal(a,cnt):
    l = np.zeros(N+1)
    flg = np.zeros(M)
    for i in range(len(a)):
        l[a[i][0]:a[i][1]] += 1
    tmp = l.argmax()
    cnt += 1
    #print("tmp:"+str(tmp))
    #tmpを区間に含むリストにフラグを立てる
    tmp_index = []
    for j in range(len(a)):
        if a[j][0]<=tmp<a[j][1]:
            #print(j)
            tmp_index.append(j)
    #print(tmp_index)
    if len(tmp_index)>0:
        for k in range(len(tmp_index)-1,-1,-1):
            #print(k)
            a.pop(tmp_index[k])
    #print(a)
    if len(a)<=0:
        return cnt
    else:
        return cal(a,cnt)
print(cal(a,0))