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>

int compare_int(const void *a, const void *b){
    //昇順
    /* if(*(int*)a > *(int*)b) return 1;
    return -1;*/
    //降順
    if(*(int*)a < *(int*)b) return 1;
    return -1;
}

int main(){

    int n;
    scanf("%d",&n);
    int a[n],b[n];
    for(int i=0;i<n;i++){
        scanf("%d",&a[i]);
        b[i]=-1;
    }

    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            if(a[i]<b[j] || b[j]<0){
                if(b[j-1]<a[i]){
                    b[j-1]=a[i];
                }else{
                    b[j]=a[i];
                }
                
                break;
            }
            
        }
        
    }

    int count=0;
    for(int i=0;i<n;i++){
        if(b[i]>=0){
            count++;
        }
    }    
    printf("%d\n",count);

    return 0;
}