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: Wrong Answer)

#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
//for(int i = 0; i < n; i++)

int main()
{
	int n;
    cin>>n;
    vector<int> a(n);
    for(int i = 0; i < n; i++)cin>>a[i];
    vector<int> color(n,0);
    int c = 1;
    while(true){
        int b = 0;
        for(int i = 0; i < n; i++){
            
            if(color[i]>0) continue;
            if(a[i] > b){
            //    cout << a[i] << endl;
            //    cout << c << endl;
                
                color[i] = c;
                b = a[i];
            }
        }
        c++;
       // cout << c << endl;
        if(c == n) break;
    }
    int ans = 0;
    for(int i = 0; i < n; i++) ans = max(ans, color[i]);
    cout << ans << endl;
	return 0;
}