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.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();
            }

            // 各色ごとの最小数を入れて置く
            var colors = new List<int>();
            // はじめの色は問答無用でセット
            colors.Add(a[0]);
            // 直前の値
            var prev = a[0];
            for (int i = 1; i < a.Length; i++)
            {
                if (prev < a[i])
                {
                    // 前よりも大きかったら、前と同じ色
                }
                else
                {
                    var min = colors.Min();
                    if (min <= a[i])
                    {
                        // どの色の最小値よりも小さかったら、色を足す
                        colors.Add(a[i]);
                    }
                    else
                    {
                        // そうでなかったら、すでに使った色を使える
                    }
                }
                prev = a[i];
            }

            Console.WriteLine($"{colors.Count}");
        }

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