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: Wrong Answer)

#include <stdio.h>
int main(void){
  long i,ans=1,color=1;

  long n;
  scanf("%ld",&n);

  long a[n];
  scanf("%ld",&a[0]);
  for(i=1;i<n;i++){
    scanf("%ld",&a[i]);
    if(a[i]<=a[i-1]){
      color++;
    }else{
      if(color>ans){
        ans=color;
      }
      color=1;
    }
  }

  if(color>ans){
    printf("%ld\n",color);
  }else{
    printf("%ld\n",ans);
  }

  return 0;
}