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>
int main(void){
    int N;
    scanf("%d", &N);
    int a[N];
    a[0]=0;
    for (int i=0; i<N; i++){
        scanf("%d", &a[i]);
    }
    int max[N];
    int color = 0;
    int flag = 0;
    max[0] = a[0];
    for(int i=1; i<N; i++){
        for(int j=0; j <= color; j++){
            flag = 0;
            if(max[j] < a[i]){
                max[j] = a[i];
                flag = 1; break;
            }
        }
        if(flag == 0){
            color += 1;
            max[color] = a[i];
        }
    }
    printf("%d\n", color+1);
    return 0; 
}