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: Wrong Answer)

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

namespace abc134_e
{
    static class Program
    {
        static void Main(string[] args)
        {
            var n = Console.ReadLine().ToInteger();
            var a = new int[n];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = Console.ReadLine().ToInteger();
            }

            // 各色の最大値(最後の値)を入れて置く<最大値, 最大値の個数>
            var colors = new SortedList<int, int>(new Comparer<int>((x, y) => x.CompareTo(y) * -1));
            colors.Add(a[0], 1);
            for (int i = 1; i < a.Length; i++)
            {
                // 各色の最後の値より大きいものの中で、最大の値を採用
                // どの色の最後の値よりも小さかったら、色を足す。
                var color = colors.FirstOrDefault(m => m.Key < a[i]);
                if (color.Key > 0)
                {
                    colors[color.Key] -= 1;
                    if (colors[color.Key] <= 0)
                    {
                        colors.Remove(color.Key);
                    }
                }
                if (colors.ContainsKey(a[i]))
                {
                    colors[a[i]] += 1;
                }
                else
                {
                    colors.Add(a[i], 1);
                }
            }

            Console.WriteLine($"{colors.Sum(m => m.Value)}");
        }

        static int ToInteger(this string s)
        {
            return int.Parse(s);
        }

        static int Compare(int x, int y)
        {
            return x.CompareTo(y) * -1;
        }
    }

    class Comparer<T> : IComparer<T>
    {
        private Func<T, T, int> compare = (x, y) => 0;

        public Comparer(Func<T, T, int> compare)
        {
            this.compare = compare;
        }

        public int Compare(T x, T y)
        {
            return compare(x, y);
        }
    }
}