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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>

int main(){
  int n,ans;
  scanf("%d",&n);
  
  int a[n+1];
  int b[n][n];
  int c[n];
  for(int i=1;i<=n;i++){
    scanf("%d",&a[i]);
    b[i][1]=a[i];
  }
  
  for(int i=2;i<=n;i++){
    b[0][i]=-1;
    b[1][i]=-1;
    c[i]=0;
  }
  
  for(int i=2;i<=n;i++){
    if(b[i][1]<=b[i-1][1]){
      for(int j=2;j<=n;j++){
        if(b[i][1]>b[c[j]][j]){
          b[c[j]+1][j]=b[i][1];
          c[j]=c[j]+1;
          break;
        }
      }
      b[i][1]=b[i-1][1];
    }
  }
  
  ans=0;
  for(int i=1;i<=n;i++){
    if(b[1][i]>=0){
      ans=ans+1;
    }
  }
  
  printf("%d",ans);
  return 0;
}