#include <iostream>
#include <map>
#include <stdexcept>
#include <cmath>

#include <boost/numeric/ublas/vector_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>

#include <boost/assert.hpp>

using namespace std ;
using namespace boost::numeric::ublas ;

typedef unsigned int AFF_index ;

typedef mapped_vector<AFF_index> AFF_noise_internal ;

class AFF_noise : public AFF_noise_internal {
	public:

	const AFF_index power() const {
		AFF_index tot = 0 ;
		AFF_noise::const_iterator it(begin()) ;
		for(;it!=end();++it) tot += *it ;
		return tot ;
	}

	const AFF_index operator()(const AFF_index& i) const {
		if(i >= size()) return 0 ;
		return AFF_noise_internal::operator()(i) ;
	}

	const AFF_index operator[](const AFF_index& i) const {
		if(i >= size()) return 0 ;
		return AFF_noise_internal::operator[](i) ;
	}

	AFF_index& operator()(const AFF_index& i) {
		if(i >= size()) resize(i+1, true) ;
		return AFF_noise_internal::operator()(i) ;
	}

	AFF_index& operator[](const AFF_index& i) {
		if(i >= size()) resize(i+1, true) ;
		return AFF_noise_internal::operator[](i) ;
	}

	AFF_noise() : AFF_noise_internal() { } ;

	AFF_noise(const AFF_index& i) : AFF_noise_internal(i+i, 1) {
		operator()(i) = 1 ;
	}

	AFF_noise(const AFF_noise& i) : AFF_noise_internal(i) {
	}

	AFF_noise& operator+=(const AFF_noise& other) {
		AFF_noise::const_iterator it ;
		if (size() < other.size()) resize(other.size(), true) ;
		for(it=other.begin(); it!=other.end(); ++it) {
			operator()(it.index()) += *it ;
		}
		return *this ;
	}

	inline AFF_noise operator+(const AFF_noise& other) const {
		AFF_noise sum = AFF_noise(*this) ;
		sum += other ;
		return sum ;
	}

	// Lexicographical sorting
	bool operator<(const AFF_noise& other) const {
		AFF_noise::const_iterator it ;
		for(it=begin(); it!=end(); ++it) {
			if(*it < other(it.index())) return true ;
			if(*it > other(it.index())) return false ;
		}
		return false ;
	}

	bool operator==(const AFF_noise& other) const {
		if (this->size() != other.size()) return false ;
		AFF_noise::const_iterator it ;
		for(it=begin(); it!=end(); ++it) {
			if(*it != other(it.index())) return false ;
		}
		return true ;
	}
} ;