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: Runtime Error)

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

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<最後の値, 色の個数>
            var colors = new SortedList<int, int>();
            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か判定する
                var count = colors.Count;
                // 一番大きいものの後ろにつけるのが効率がいいので、後ろから判定する
                for (int c = 0; c < count; c++)
                {
                    var index = count - c - 1;
                    var color = colors.Keys[index];
                    if (a[i] > color)
                    {
                        // 大きい色があったら、その色を採用
                        colors[color]--;
                        break;
                    }
                }

                // どの色の最後の値よりも小さかったら、色を足す。
                if (colors.Keys.Contains(a[i]))
                {
                    colors[a[i]]++;
                }
                else
                {
                    colors.Add(a[i], i);
                }
            }

            Console.WriteLine($"{colors.Values.Sum()}");
        }

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