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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static Common;

public static class Common
{
    public static int BinSearchIndex<T>(T v, IEnumerable<T> list)
        where T : IComparable
    {
        int minRange = 0;
        int maxRange = list.Count();
        while (minRange != maxRange)
        {
            var center = (minRange + maxRange) / 2;
            if (list.ElementAt(center).CompareTo(v) < 0)
            {
                minRange = center + 1;
            }
            else
            {
                maxRange = center;
            }
        }

        return minRange;
    }
}

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 list = new List<int>();
        foreach (var a in A.Reverse())
        {
            var index = BinSearchIndex(a + 1, list);
            if (index < list.Count)
            {
                list[index] = a;
            }
            else
            {
                list.Add(a);
            }
        }

        Console.WriteLine(list.Count);
    }
}