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;

namespace ABC134
{
    class abc134e
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var a = new List<int>();
            for (var i = 0; i != n; ++i) {
                a.Add(int.Parse(Console.ReadLine()));
            }

            var maxInColor = new List<int>();
            foreach (var v in a) {
                var addColor = true;
                for(var i = maxInColor.Count; i != 0; --i) {
                    if (v > maxInColor[i - 1]) {
                        maxInColor[i - 1] = v;
                        addColor = false;
                        break;
                    }
                }
                if (addColor)
                    maxInColor.Add(v);
            }

            Console.WriteLine(maxInColor.Count);
        }
    }
}