Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int binsearch(long *ary, long val, int imin, int imax){
  while(1){
    int imid=imin+(imax-imin)/2;
    if(ary[imid]<val && ary[imid+1]>=val) return imid;
    else if(ary[imid]>=val) imax=imid-1;
    else imin=imid+1;
  }
}

int main()
{
  int i, j, k, n;
  long a[100000];
  long bicolor[300020];
  long *color= &bicolor[100010];
  int numcolor=0;
  scanf("%d", &n);
  for(i=0;i<n;i++){
    scanf("%ld", &a[i]);
    if(numcolor==0){
      color[numcolor]=a[i];
      numcolor++;
    }else{
      if(a[i]<=color[0]){
//        for(j=numcolor; j>0; j--){
//          color[j]=color[j-1];
//        }
        color--;
        color[0]=a[i];
        numcolor++;
      }else{
        color[numcolor]=1000000001;
        j=binsearch(color,a[i],0,numcolor-1);
        color[j]=a[i];
      }
    }
  }

  printf("%d\n", numcolor);

  return 0;
}