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)

// abc134c: Exception Handling
#include <stdio.h>

int search(int k, int *a, int n){
  int l=0,r=n,m;
  while(l<r){ m=(l+r)/2; if(a[m]<k) r=m; else l=m+1; }
  return l;
}

int main(){
  int n;scanf("%d",&n);
  int gn = 1, g[n];scanf("%d",g);
  for(int i=1;i<n;i++){
    int a;scanf("%d",&a);
    int j = search(a,g,gn);
    g[ j<gn? j: gn++ ] = a;
  }
  printf("%d\n",gn);
  return 0;
}