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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public class Solution
{
    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var A = new int[N];
        for (int i = 0; i < N; i++)
        {
            A[i] = int.Parse(Console.ReadLine());
        }
        var used = new bool[N];

        int count = 0;
        for (int i = 0; i < N; i++)
        {
            if (used[i])
            {
                continue;
            }
            used[i] = true;
            count++;
            var v = A[i];
            for (int j = i + 1; j < N; j++)
            {
                if (!used[j] && v < A[j])
                {
                    v = A[j];
                    used[j] = true;
                }
            }
        }

        Console.WriteLine(count);
    }
}