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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int main(){
  int n;
  scanf("%d",&n);
  long a[100000];
  long b[100000];
  int flag[100000] = {};
  int i;
  for(i=0;i<n;i++){
    scanf("%ld",&a[i]);
  }
  int answer = 0;
  int j;
  long tmp;
  for(i=0;i<n;i++){
    if(flag[i] == 0){
      answer += 1;
      flag[i] = 1;
      tmp = a[i];
      for(j=i+1;j<n;j++){
        if(tmp < a[j] && flag[j] == 0){
          flag[j] = 1;
          tmp = a[j];
        }
      }
    }
  }
  printf("%d",answer);
  return 0;
}