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;

public class Hello
{
    private const int MOD_N = 1000000000 + 7;

    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var ass = new int[n];
        for (int i = 0; i < ass.Length; ++i)
        {
            ass[i] = int.Parse(Console.ReadLine());
        }

        int count = 1;
        var dec = new int[n];
        dec[0] = ass[0];

        for (int i = 1; i < ass.Length; ++i)
        {
            var a = ass[i];
            int lower = -1, upper = count;

            while (true)
            {
                var index = (upper + lower) / 2;

                if (dec[index] < a)
                {
                    upper = index;
                }
                else
                {
                    lower = index;
                }

                if (upper - lower == 1)
                {
                    dec[upper] = a;
                    if (upper == count)
                        ++count;
                    break;
                }
            }
        }

        Console.WriteLine(count);
    }

    private static int GCD(int a, int b) => a > b ? GCD_impl(a, b) : GCD_impl(b, a);
    private static int GCD_impl(int a, int b) => b == 0 ? a : GCD_impl(b, a % b);
    private static long LCM(int a, int b) => (long)a * b / GCD(a, b);

    private static int Comb(int m, int n)
    {
        var t = m - n;
        if (n > t)
            n = t;

        long numerator = 1;
        for (int i = 0; i < n; ++i)
        {
            numerator *= m - i;
            numerator %= MOD_N;
        }
        long denominator = 1;
        for (; n != 0; --n)
        {
            denominator *= n;
            denominator %= MOD_N;
        }

        var inv_denominator = ModInv((int)denominator, MOD_N);
        var ret = (int)(numerator * inv_denominator % MOD_N);

        return ret >= 0 ? ret : ret + MOD_N;
    }

    private static int ModInv(int a, int m)
    {
        int b = m, x = 1, y = 0;
        while (b != 0)
        {
            var t = a / b;
            a -= t * b;
            Swap(ref a, ref b);
            x -= t * y;
            Swap(ref x, ref y);
        }
        x %= m;
        return x >= 0 ? x : x + m;
    }

    private static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
}