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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#define SIZE 100000
void Swap(int a[],int b[],int i,int j);
void Qsort(int a[],int b[],int bottom,int up);

int main(){
  int n,m,a[SIZE],b[SIZE];
  int i;
  int x,counter=1;
  scanf("%d%d",&n,&m);
  for(i=0;i<m;i++){
    scanf("%d%d",&a[i],&b[i]);
  }
  Qsort(a,b,0,m-1);
  x=b[0]-1;
  for(i=1;i<m;i++){
    if(x<a[i]){
      counter++;
      x=b[i]-1;
    }
  }
  printf("%d\n",counter);


  return 0;
}

void Swap(int a[],int b[],int i,int j){
  int temp;
  temp=a[i];
  a[i]=a[j];
  a[j]=temp;
  temp=b[i];
  b[i]=b[j];
  b[j]=temp;
}  

void Qsort(int a[],int b[],int bottom,int up){
  int i,j,k;
  int pivot;
  
  i=bottom;
  j=up;
  pivot=b[(bottom+up+1)/2];
  
  while(1){
    while(b[i]<pivot) i++; //左からpivot以上をサーチ
    while(b[j]>pivot) j--; //右からpivot以下をサーチ
    if(i>=j) break; //左が右と交差したら終了
    
    Swap(a,b,i,j);
    i++;
    j--;
  }
  if(bottom<i-1) Qsort(a,b,bottom,i-1); //分割した左の要素が2つ以上なら左でQsort
  if(i<up) Qsort(a,b,i,up); //分割した右の要素2つ以上なら右でsort
}