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;

class Program {
    static int ReadInt() { return int.Parse(Console.ReadLine()); }
    static int[] ReadInts() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    static string[] ReadStrings() { return Console.ReadLine().Split(); }

    static int LowerBound(int[] xs, int value) {
        int lo = 0;
        int hi = xs.Length - 1;
        int lower = xs.Length;
        while (lo <= hi) {
            int m = (lo + hi) / 2;
            if (value <= xs[m]) {
                lower = Math.Min(lower, m);
                hi = m - 1;
            }
            else {
                lo = m + 1;
            }
        }
        return lower;
    }

    static int Len(int[] xs) {
        int n = xs.Length;
        var dp = new int[n + 1];
        for (int i = 0; i < dp.Length; i++)
            dp[i] = int.MaxValue;

        foreach (int x in xs) {
            int p = Array.BinarySearch(dp, x);
            if (p < 0) {
                dp[~p] = x;
            }
        }
        return LowerBound(dp, int.MaxValue);
    }

    static void Main() {
        int n = ReadInt();
        var xs = new int[n];
        for (int i = 0; i < n; i++) {
            xs[i] = ReadInt();
        }

        var ans = Len(xs);
        Console.WriteLine(ans);
    }
}