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.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
		static void Main(){
		Sc sc=new Sc();
		var n=sc.I;
		int ans=0;
		var avl=new Avl();
		for(int i = 0;i<n;i++) {
			int a=sc.I;
			var p=avl.Ub(a-1);
			if(p==null){ans++;}
			else{
				avl.Dl(p.n);
			}
			avl.Ud(a);
		}
		Console.WriteLine("{0}",ans);
	}
}

public class Avl{
	public class Nd{
		public int h=1,c=1;
		public readonly int n;
		public Nd l,r;
		public Nd(int n,Nd l,Nd r){this.n=n;this.l=l;this.r=r;}
	}
	public Nd root,du;
	public int cnt=0;
	public Avl(){
		du=new Nd(int.MinValue,du,du);du.h=0;du.c=0;
		root=du;
	}
	public void Ud(int n){
		Nd mn=new Nd(n,du,du);
		if(root==du){root=mn;}
		else{
			Fu(root,n,mn);
			if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
		}
		cnt++;
	}
	private void Fu(Nd t,int n,Nd mn){
		t.c++;
		if(t.n>n){
			if(t.l!=du){
				Fu(t.l,n,mn);
				if(Abs(t.l.l.h-t.l.r.h)>1){t.l=Rotate(t.l);}
			}
			else{t.l=mn;}
		}
		else{
			if(t.r!=du){
				Fu(t.r,n,mn);
				if(Abs(t.r.l.h-t.r.r.h)>1){t.r=Rotate(t.r);}
			}
			else{t.r=mn;}
		}
		t.h=Max(t.l.h,t.r.h)+1;
	}
	private Nd Rotate(Nd t){
		Nd nd=du;
		if(t.l.h>t.r.h){
			if(t.l.l.h>t.l.r.h){
				nd=t.l;t.l=t.l.r;nd.r=t;
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
			}
			else{
				nd=t.l.r;
				t.l.r=nd.l;nd.l=t.l;
				t.l.h=Max(t.l.l.h,t.l.r.h)+1;
				t.l.c=t.l.l.c+t.l.r.c+1;
				t.l=nd.r;nd.r=t;
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
			}
		}
		else{
			if(t.r.l.h>t.r.r.h){
				nd=t.r.l;
				t.r.l=nd.r;nd.r=t.r;
				t.r.h=Max(t.r.l.h,t.r.r.h)+1;
				t.r.c=t.r.l.c+t.r.r.c+1;
				t.r=nd.l;nd.l=t;
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
			}
			else{
				nd=t.r;t.r=t.r.l;nd.l=t;
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
			}
		}
		nd.h=Max(nd.l.h,nd.r.h)+1;
		nd.c=nd.l.c+nd.r.c+1;
		return nd;
	}
	public bool Dl(int n){
		Nd t=root;
		if(t.n==n){
			root=Fd2(root);
			if(cnt==0){return true;}
			else if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
			else{
				root.h=Max(root.l.h,root.r.h)+1;
				root.c=root.l.c+root.r.c+1;
			}
			return true;
		}
		bool bo=Fd1(root,n);
		if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
		else{
			root.h=Max(root.l.h,root.r.h)+1;
			root.c=root.l.c+root.r.c+1;
		}
		return bo;
	}
	private bool Fd1(Nd t,int n){
		if(t.n>n){
			if(t.l==du){return false;}
			else if(t.l.n!=n){
				bool bo=Fd1(t.l,n);
				if(Abs(t.l.l.h-t.l.r.h)>1){t.l=Rotate(t.l);}
				else{
					t.l.h=Max(t.l.l.h,t.l.r.h)+1;
					t.l.c=t.l.l.c+t.l.r.c+1;
				}
				return bo;
			}
			else{
				t.l=Fd2(t.l);
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
				return true;
			}
		}
		else{
			if(t.r==du){return false;}
			else if(t.r.n!=n){
				bool bo=Fd1(t.r,n);
				if(Abs(t.r.l.h-t.r.r.h)>1){t.r=Rotate(t.r);}
				else{
					t.r.h=Max(t.r.l.h,t.r.r.h)+1;
					t.r.c=t.r.l.c+t.r.r.c+1;
				}
				return bo;
			}
			else{
				t.r=Fd2(t.r);
				t.h=Max(t.l.h,t.r.h)+1;
				t.c=t.l.c+t.r.c+1;
				return true;
			}
		}
	}
	private Nd Fd2(Nd dn){
		cnt--;
		if(dn.l==du){return dn.r;}
		if(dn.r==du){return dn.l;}
		Nd u=dn.l;
		if(u.r==du){
			u.r=dn.r;
			u.h=Max(u.l.h,u.r.h)+1;
			u.c=u.l.c+u.r.c+1;
			return u;
		}
		u=Fd3(u,dn);
		if(Abs(dn.l.l.h-dn.l.r.h)>1){u.l=Rotate(dn.l);}
		else{
			dn.l.h=Max(dn.l.l.h,dn.l.r.h)+1;
			dn.l.c=dn.l.l.c+dn.l.r.c+1;
		}
		u.h=Max(u.l.h,u.r.h)+1;
		u.c=u.l.c+u.r.c+1;
		return u;
	}
	private Nd Fd3(Nd u,Nd dn){
		if(u.r.r!=du){
			Nd v=Fd3(u.r,dn);
			if(Abs(u.r.l.h-u.r.r.h)>1){u.r=Rotate(u.r);}
			else{
				u.r.h=Max(u.r.l.h,u.r.r.h)+1;
				u.r.c=u.r.l.c+u.r.r.c+1;
			}
			return v;
		}
		else{
			Nd v=u.r;u.r=u.r.l;v.l=dn.l;v.r=dn.r;
			return v;
		}
	}
	public bool Hs(int n){
		Nd t=root;
		if(cnt==0){return false;}
		if(t.n==n){return true;}
		bool bo=false;
		while(true){
			if(t.n>n){
				if(t.l==du){break;}
				else if(t.l.n!=n){t=t.l;}
				else{bo=true;break;}
			}
			else{
				if(t.r==du){break;}
				else if(t.r.n!=n){t=t.r;}
				else{bo=true;break;}
			}
		}
		return bo;
	}
	public Nd Ra(int n){return cnt>=n?Fr(root,n):null;}
	private Nd Fr(Nd t,int n){
		if(t.l.c>n-1){return Fr(t.l,n);}
		if(t.l.c<n-1){return Fr(t.r,n-t.l.c-1);}
		return t;
	}
	public Nd Lb(int n){return cnt!=0?Flb(root,n):null;}
	private Nd Flb(Nd t,int n){
		if(t.n<n){
			if(t.r==du){return null;}
			return Flb(t.r,n);
		}
		if(t.n>n){
			if(t.l==du){return t;}
			Nd u=Flb(t.l,n);
			return u==null?t:u;
		}
		return t;
	}
	public Nd Ub(int n){return cnt!=0?Fub(root,n):null;}
	private Nd Fub(Nd t,int n){
		if(t.n>n){
			if(t.l==du){return null;}
			return Fub(t.l,n);
		}
		if(t.n<n){
			if(t.r==du){return t;}
			Nd u=Fub(t.r,n);
			return u==null?t:u;
		}
		return t;
	}
	public int Rg(int a,int b){return cnt!=0?Frg(root,a,b,false,false):0;}
	private int Frg(Nd t,int a,int b,bool l,bool r){
		if(t.h==0){return 0;}
		if(l&&r){return t.c;}
		if(t.n<a){return Frg(t.r,a,b,t.n>=a,r);}
		if(t.n>b){return Frg(t.l,a,b,l,t.n<=b);}
		return Frg(t.l,a,b,l,t.n<=b)+Frg(t.r,a,b,t.n>=a,r)+1;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}