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>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>

int main(void){
    int i,j,k;
    int N;
    bool color[100000] = {false};
    unsigned int A[100000],answer = 0;
    
    scanf("%d",&N);
    for(i = 0;i < N;i++){
        scanf("%d",&A[i]);
    }
    
    for(i = 0;i < N;i++){
        answer++;
        if(color[i] == true){
            answer--;
        }else{
            for(j = i+1;j < N;j++){
                if(A[i] < A[j]){
                    color[j] = true;
                }
            }
        }
    }
    
    printf("%d\n",answer);
    
    return 0;
}