Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in C# (judge verdict: Accepted)

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

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            int[] A = new int[n];

            for (int i = 0; i < n; i++)
            {
                A[i] = int.Parse(Console.ReadLine());
            }

            Console.WriteLine(GetLIS(A));
        }

        static int GetLIS(int[] A)
        {
            int n = A.Length, length = 1;

            List<int> L = new List<int>();
            L.Add(A[0]);

            for (int i = 1; i < n; i++)
            {
                if (L[length - 1] < A[i])
                {
                    L.Add(A[i]);
                    length++;
                }
                else
                {
                    int index = LowerBound(L, A[i]);
                    L[index] = A[i];
                }
            }
            return length;
        }

        static int LowerBound(List<int> arr, int value)
        {
            int low = 0;
            int high = arr.Count;
            int mid;

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