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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var A = new int[N];
            for (int i = 0; i < N; i++) A[i] = ReadInt();
            var minL = new List<int>();
            var cnt = 0;
            minL.Add(A[N - 1]);
            cnt++;
            for (int i = N - 2; i >= 0; i--)
            {
                var idx = UpperBound(minL, A[i]);
                if (idx == minL.Count())
                {
                    minL.Add(A[i]);
                    cnt++;
                }
                else
                {
                    minL[idx] = A[i];
                }
            }

            Console.WriteLine(cnt);
            Console.ReadLine();
        }

        static int UpperBound(List<int> arr, int val)
        {
            val++;
            if (arr[0] >= val) return 0;
            if (arr[arr.Count() - 1] < val) return arr.Count();

            var low = 0;
            var high = arr.Count() - 1;

            while (low + 1 < high)
            {
                var mid = (low + high) / 2;
                if (arr[mid] >= val) high = mid;
                else low = mid;
            }

            return high;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}