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: Runtime Error)

    #include <stdio.h>
    #define N 100000
     
    int main(void){
        int n;
        int a[N];
        int memo[N];
        int i,j,k,tmp;
        for(i = 0; i < N; i++){
            memo[i] = -1;
        }
        
        scanf("%d", &n);
        for(i = 0; i < n; i++){
            scanf("%d", &a[i]);
        }
        
        memo[0] = a[0];
        for(i = 1; i < n; i++){
            j = 0;
            while(a[i] <= memo[j]){
                j++;
            }
            memo[j] = a[i];
            tmp = memo[j];
            k = j;
            while(tmp > memo[k] && k >= 1){
                memo[k] = memo[k-1];
                k--;
            }
            memo[k] = tmp;
        }
        
        for(i = 0; ; i++){
            if(memo[i] == -1){
                break;
            }
        }
        
        printf("%d", i);
        return 0;
    }