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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<vector>
using namespace std;

long long int devide(long long int input[100000], long int n){
    long long int max = -1;
    long long int devided_input[n];
    long int count_devided_input=0;
    if(n == 0){
        return 0;
    }
    for(int i=0; i<n; i++){
        if(max < input[i]){
            max = input[i];
        }else{
            devided_input[count_devided_input] = input[i];
            count_devided_input++;
        }
    }
    return 1 + devide(devided_input, count_devided_input);
}

int main()
{
    long int N, vector_count;
    long long int num;
    long long int input[100000];
    cin >> N;
    for(long int i=0; i<N; i++){
        cin >> input[i];
    }
    cout <<  devide(input, N);
    return 0;
}