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 <string.h>

int main(void){
    long long int n;
    long long int min=1000000002;
    long long int next=0;
    long long int a[20005000];
    long long int color[100000];
    long long int ans;
    long long int i,k;
    long long int count=0;
    long long int j, increment, temp, temp_b;
    increment = 8;
    long long int b[100000];
    long long int array_size;
    
    scanf("%lld",&n);
    for (i=0; i<n; i++){
        scanf("%lld", &a[i]);
        
        if(a[i]<=min){
            //new
            color[count]=a[i];
            count++;
        }else{
            for(k=0; k<=count; k++){
                if(color[count-k]>=a[i]){
                    color[count-k]=a[i];
                    break;
                }
            }
        }
        
        //sort
        array_size = count;
        while (increment > 0){
            for (i=0; i < array_size; i++){
                j = i;
                temp = color[i];
                temp_b = b[i];
                while ((j >= increment) && (color[j-increment] > temp)){
                    color[j] = color[j - increment];
                    b[j] = b[j - increment];
                    j = j - increment;
                }
                color[j] = temp;
                b[j] = temp_b;
            }
            if (increment/2 != 0)
                increment = increment/2;
            else if (increment == 1)
                increment = 0;
            else
                increment = 1;
        }
        //sort end
        
        min=color[0];
    }
    
    printf("%lld\n",count);
    return 0;
}