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){
    // Your code here!
    int n, i, j, colors[100000], color_num=0, now_k, now_v, a;
    scanf("%d", &n);
    for(i = 0; i < n; i++){
        now_k = -1;
        now_v = -1;
        scanf("%d", &a);
        for(j = 0; j < color_num; j++){
            if(colors[j] > now_v && colors[j] < a){
                now_k = j;
                now_v = colors[j];
            }
        }
        if(now_k == -1){
            colors[color_num] = a;
            color_num++;
        }else{
            colors[now_k] = a; 
        }
    }
    printf("%d", color_num);
}