bignum

int a=9<<9e9;

#include<iostream>
using namespace std;

class S
{
public:
	virtual bool next()=0;
	virtual S *dup()=0;
	virtual S *max()=0;
	virtual void dump()=0;
};

int length(S **list)
{
	if(!list)
	{
		return 0;
	}
	int i;
	for(i=0;list[i]!=0;++i);
	return i;
}

class S0 : public S
{
public:
	int i;
	virtual bool next(){return --i>0;}
	virtual S *dup()
	{
		S0 *s=new S0();
		s->i=i;
		return (S*)s;
	}
	virtual S *max()
	{
		S0 *s=new S0();
		s->i=a;
		return (S*) s;
	}
	virtual void dump()
	{
		cout<<i;
	}
};

class S1 : public S
{
public:
	S *value;
	S *rank;
	S** list;

	virtual bool next()
	{
		if(!list)
		{
			return value->next();
		}
		int i;
		for(i=0;list[i] && !list[i]->next();++i)
		{
			list[i]=list[i]->max();
		}
		if(list[i]==0)
		{
			return value->next();
		}
		return true;
	}

	virtual S *dup()
	{
		S1 *s=new S1();
		s->value=value->dup();
		s->rank=rank->dup();
		s->list=0;
		if(list)
		{
			int l=length(list);
			s->list=new S *[l+1];
			for(int i=0;i<l;++i)
			{
				s->list[i]=list[i]->dup();
			}
			s->list[l]=0;
		}
		return (S *)s;
	}

	virtual S *max()
	{
		S1 *s=new S1();
		s->value=value->max();
		s->rank=rank->dup();
		s->list=new S *[a+1];
		for(int i=0;i<a;++i)
		{
			s->list[i]=list[i]->max();
		}
		s->list[a]=0;
		return (S *)s;
	}

	virtual void dump()
	{
		cout<<"$(";
		value->dump();
		cout<<")";
		cout<<"<";
		rank->dump();
		cout<<">";
		if(list)
		{
			cout<<"[";
			for(int i=0;list[i]!=0;i++)
			{
				list[i]->dump();
				cout<<",";
			}
			cout<<"]";
		}
	}
};

S *generate(S *x,S *rank)
{
	S1 *s=new S1();
	s->value=x->dup();
	s->rank=rank->dup();
	S *r=rank->dup();
	bool n=r->next();
	if(!n)
	{
		s->list=0;
	}
	else
	{
		s->list=new S *[a+1];
		for(int i=0;i<a;++i)
		{
			s->list[i]=generate(x,r);
		}
		s->list[a]=0;
	}
	return s;
}

S *generate2()
{
	S0 s0;
	S *s=generate(s0.max(),s0.max());
	for(int i=0;i<a;i++)
	{
		s=generate(s->max(),s->max());
	}
	return s;
}

void f(S *s)
{
	a<<=a<<a;
	if(!s->next())
	{
		return;
	}
	S *m=generate2();
	while(m->next())
	{
		f(s->dup());
	}
}

int main()
{
	f(generate2());
	return a;
}