You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]



#include "./standard_include.cpp"
#define unlikely -214741

#include "set_parameters.cpp"








/*
 void printmcs(deque<set<int> > & A, deque<set<int> > & B) {
 
 for(int i=0; i<A.size(); i++) {
 
 for(set<int>::iterator its=A[i].begin(); its!=A[i].end(); its++) 
 if(*its==i)
 cherr(2111);
 
 
 
 }
 
 
 for(int i=0; i<A.size(); i++) {
 
 for(set<int>::iterator its=A[i].begin(); its!=A[i].end(); its++) 
 if(B[*its].find(i)==B[*its].end())
 cherr(2111);
 
 }
 
 
 cout<<"printmcs passed"<<endl;
 
 
 }
 
 //*/


// it computes the sum of a deque<int>

int deque_int_sum(const deque<int> & a) {
	
	int s=0;
	for(int i=0; i<a.size(); i++)
		s+=a[i];
    
	return s;
}

// it computes the integral of a power law
double integral (double a, double b) {
    
	
	if (fabs(a+1.)>1e-10)
		return (1./(a+1.)*pow(b, a+1.));
	
	
	else
		return (log(b));
    
}


// it returns the average degree of a power law
double average_degree(const double &dmax, const double &dmin, const double &gamma) {
    
	return (1./(integral(gamma, dmax)-integral(gamma, dmin)))*(integral(gamma+1, dmax)-integral(gamma+1, dmin));
    
}


//bisection method to find the inferior limit, in order to have the expected average degree
double solve_dmin(const double& dmax, const double &dmed, const double &gamma) {
	
	double dmin_l=1;
	double dmin_r=dmax;
	double average_k1=average_degree(dmin_r, dmin_l, gamma);
	double average_k2=dmin_r;
	
	
	if ((average_k1-dmed>0) || (average_k2-dmed<0)) {
		
		cerr<<"\n***********************\nERROR: the average degree is out of range:";
		
		if (average_k1-dmed>0) {
			cerr<<"\nyou should increase the average degree (bigger than "<<average_k1<<")"<<endl; 
			cerr<<"(or decrease the maximum degree...)"<<endl;
		}
		
		if (average_k2-dmed<0) {
			cerr<<"\nyou should decrease the average degree (smaller than "<<average_k2<<")"<<endl; 
			cerr<<"(or increase the maximum degree...)"<<endl;
		}
		
		return -1;	
	}
	
    
	while (fabs(average_k1-dmed)>1e-7) {
		
		double temp=average_degree(dmax, ((dmin_r+dmin_l)/2.), gamma);
		if ((temp-dmed)*(average_k2-dmed)>0) {
			
			average_k2=temp;
			dmin_r=((dmin_r+dmin_l)/2.);
            
		}
		else {
			
			average_k1=temp;
			dmin_l=((dmin_r+dmin_l)/2.);
			
            
		}
        
		
        
        
	}
	
	return dmin_l;
}



// it computes the correct (i.e. discrete) average of a power law
double integer_average (int n, int min, double tau) {
	
	double a=0;
    
	for (double h=min; h<n+1; h++)
		a+= pow((1./h),tau);
	
	
	double pf=0;
	for(double i=min; i<n+1; i++)
		pf+=1/a*pow((1./(i)),tau)*i;
	
	return pf;
    
}



// this function changes the community sizes merging the smallest communities
int change_community_size(deque<int> &seq) {
    
	
    
	if (seq.size()<=2)
		return -1;
	
	int min1=0;
	int min2=0;
	
	for (int i=0; i<seq.size(); i++)		
		if (seq[i]<=seq[min1])
			min1=i;
	
	if (min1==0)
		min2=1;
	
	for (int i=0; i<seq.size(); i++)		
		if (seq[i]<=seq[min2] && seq[i]>seq[min1])
			min2=i;
	
    
	
	seq[min1]+=seq[min2];
	
	int c=seq[0];
	seq[0]=seq[min2];
	seq[min2]=c;
	seq.pop_front();
	
	
	return 0;
}









int build_bipartite_network(deque<deque<int> >  & member_matrix, const deque<int> & member_numbers, const deque<int> &num_seq) {
    
	
	
	// this function builds a bipartite network with num_seq and member_numbers which are the degree sequences. in member matrix links of the communities are stored
	// this means member_matrix has num_seq.size() rows and each row has num_seq[i] elements
	
	
	
	deque<set<int> > en_in;			// this is the Ein of the subgraph
	deque<set<int> > en_out;		// this is the Eout of the subgraph
	
	
	{
    set<int> first;
    for(int i=0; i<member_numbers.size(); i++) {
        en_in.push_back(first);
    }
	}
	
	{
    set<int> first;
    for(int i=0; i<num_seq.size(); i++) {
        en_out.push_back(first);
    }
	}
    
	
	
	multimap <int, int> degree_node_out;
	deque<pair<int, int> > degree_node_in;
	
	for(int i=0; i<num_seq.size(); i++)
		degree_node_out.insert(make_pair(num_seq[i], i));
	
	for(int i=0; i<member_numbers.size(); i++)
		degree_node_in.push_back(make_pair(member_numbers[i], i));
	
	
	sort(degree_node_in.begin(), degree_node_in.end());
	
	
	
	deque<pair<int, int> >::iterator itlast = degree_node_in.end();
	
	/*
     for (int i=0; i<degree_node_in.size(); i++)
     cout<<degree_node_in[i].first<<" "<<degree_node_in[i].second<<endl;
     */
	
	
	
	while (itlast != degree_node_in.begin()) {
		
		itlast--;
		
		
		multimap <int, int>::iterator itit= degree_node_out.end();
		deque <multimap<int, int>::iterator> erasenda;
		
		for (int i=0; i<itlast->first; i++) {
			
			if(itit!=degree_node_out.begin()) {
				
				itit--;
				
                
				en_in[itlast->second].insert(itit->second);
				en_out[itit->second].insert(itlast->second);
                
				erasenda.push_back(itit);
				
			}
			
			else
				return -1;
            
		}
		
		
		//cout<<"degree node out before"<<endl;
		//prints(degree_node_out);
		
		for (int i=0; i<erasenda.size(); i++) {
			
			
			if(erasenda[i]->first>1)
				degree_node_out.insert(make_pair(erasenda[i]->first - 1, erasenda[i]->second));
            
			
			degree_node_out.erase(erasenda[i]);
            
			
            
		}
		
		//cout<<"degree node out after"<<endl;
		//prints(degree_node_out);
		
	}
	
	
	// this is to randomize the subgraph -------------------------------------------------------------------
    
    
    deque<int> degree_list;
    for(int kk=0; kk<member_numbers.size(); kk++)
        for(int k2=0; k2<member_numbers[kk]; k2++)
            degree_list.push_back(kk); 
    
	
	for(int run=0; run<10; run++) for(int node_a=0; node_a<num_seq.size(); node_a++) for(int krm=0; krm<en_out[node_a].size(); krm++) {
        
        int random_mate=degree_list[irand(degree_list.size()-1)];
		
		if (en_out[node_a].find(random_mate)==en_out[node_a].end()) {
			
			deque <int> external_nodes;
			for (set<int>::iterator it_est=en_out[node_a].begin(); it_est!=en_out[node_a].end(); it_est++)
				external_nodes.push_back(*it_est);
            
            
			int	old_node=external_nodes[irand(external_nodes.size()-1)];
            
			
			deque <int> not_common;
			for (set<int>::iterator it_est=en_in[random_mate].begin(); it_est!=en_in[random_mate].end(); it_est++)
				if (en_in[old_node].find(*it_est)==en_in[old_node].end())
					not_common.push_back(*it_est);
            
			
			if (not_common.empty())
				break;
            
			int node_h=not_common[irand(not_common.size()-1)];
			
			
			en_out[node_a].insert(random_mate);
			en_out[node_a].erase(old_node);
			
			en_in[old_node].insert(node_h);
			en_in[old_node].erase(node_a);
			
			en_in[random_mate].insert(node_a);
			en_in[random_mate].erase(node_h);
			
			en_out[node_h].erase(random_mate);
			en_out[node_h].insert(old_node);
			
            
		}	
	}
    
	
	
	member_matrix.clear();
	deque <int> first;
	
	for (int i=0; i<en_out.size(); i++) { 
		
		member_matrix.push_back(first);
		for (set<int>::iterator its=en_out[i].begin(); its!=en_out[i].end(); its++)
			member_matrix[i].push_back(*its);
        
	}
	
	
	return 0;
    
    
}



int internal_degree_and_membership (double mixing_parameter, int overlapping_nodes, int max_mem_num, int num_nodes, deque<deque<int> >  & member_matrix, 
                                    bool excess, bool defect,  deque<int> & degree_seq_in, deque<int> & degree_seq_out, deque<int> &num_seq, deque<int> &internal_degree_seq_in, deque<int> &internal_degree_seq_out, bool fixed_range, int nmin, int nmax, double tau2) {
	
	
	
	
	if(num_nodes< overlapping_nodes) {
		
		cerr<<"\n***********************\nERROR: there are more overlapping nodes than nodes in the whole network! Please, decrease the former ones or increase the latter ones"<<endl;
		return -1;
	}
	
	
	// 
	member_matrix.clear();
	internal_degree_seq_in.clear();
	
	deque<double> cumulative;
	
	// it assigns the internal degree to each node -------------------------------------------------------------------------
	int max_degree_actual=0;		// maximum internal degree
    
	for (int i=0; i<degree_seq_in.size(); i++) {
		
		double interno=(1-mixing_parameter)*degree_seq_in[i];
		int int_interno=int(interno);
		
		
		if (ran4()<(interno-int_interno))
			int_interno++;
		
		if (excess) {
			
			while (   (  double(int_interno)/degree_seq_in[i] < (1-mixing_parameter) )  &&   (int_interno<degree_seq_in[i])   )
				int_interno++;
            
            
		}
		
		
		if (defect) {
			
			while (   (  double(int_interno)/degree_seq_in[i] > (1-mixing_parameter) )  &&   (int_interno>0)   )
				int_interno--;
            
            
		}
        
		
		
		
		internal_degree_seq_in.push_back(int_interno);
		
		
		if (int_interno>max_degree_actual)
			max_degree_actual=int_interno;
		
        
	}
	
	for (int i=0; i<degree_seq_out.size(); i++) {
		
		double interno=(1-mixing_parameter)*degree_seq_out[i];
		int int_interno=int(interno);
		
		
		if (ran4()<(interno-int_interno))
			int_interno++;
		
		if (excess) {
			
			while (   (  double(int_interno)/degree_seq_out[i] < (1-mixing_parameter) )  &&   (int_interno<degree_seq_out[i])   )
				int_interno++;
            
            
		}
		
		
		if (defect) {
			
			while (   (  double(int_interno)/degree_seq_out[i] > (1-mixing_parameter) )  &&   (int_interno>0)   )
				int_interno--;
            
            
		}
        
		
		internal_degree_seq_out.push_back(int_interno);
        
	}
	
	// it assigns the community size sequence -----------------------------------------------------------------------------
	
	powerlaw(nmax, nmin, tau2, cumulative);
	
	
	if (num_seq.empty()) {
		
		int _num_=0;
		if (!fixed_range && (max_degree_actual+1)>nmin) {
            
			_num_=max_degree_actual+1;			// this helps the assignment of the memberships (it assures that at least one module is big enough to host each node)
			num_seq.push_back(max_degree_actual+1);
            
		}
		
		
		while (true) {
			
			
			int nn=lower_bound(cumulative.begin(), cumulative.end(), ran4())-cumulative.begin()+nmin;
			
			if (nn+_num_<=num_nodes + overlapping_nodes * (max_mem_num-1) ) {
				
				num_seq.push_back(nn);				
				_num_+=nn;
                
			}
			else
				break;
			
			
		}
		
		num_seq[min_element(num_seq.begin(), num_seq.end()) - num_seq.begin()]+=num_nodes + overlapping_nodes * (max_mem_num-1) - _num_;
		
	}
	
	
	//cout<<"num_seq"<<endl;
	//prints(num_seq);
	
	int ncom=num_seq.size();
	
	//cout<<"\n----------------------------------------------------------"<<endl;
    
    
	deque<int> member_numbers;
	for(int i=0; i<overlapping_nodes; i++)
		member_numbers.push_back(max_mem_num);
	for(int i=overlapping_nodes; i<degree_seq_in.size(); i++)
		member_numbers.push_back(1);
	
	//prints(member_numbers);
	//prints(num_seq);
	
	if(build_bipartite_network(member_matrix, member_numbers, num_seq)==-1) {
		
		cerr<<"it seems that the overlapping nodes need more communities that those I provided. Please increase the number of communities or decrease the number of overlapping nodes"<<endl;
		return -1;			
        
	}
    
	
	
	//printm(member_matrix);
	
	//cout<<"degree_seq_in"<<endl;
	//prints(degree_seq_in);
	
	//cout<<"internal_degree_seq_in"<<endl;
	//prints(internal_degree_seq_in);
    
	deque<int> available;
	for (int i=0; i<num_nodes; i++)
		available.push_back(0);
	
	for (int i=0; i<member_matrix.size(); i++) {
		for (int j=0; j<member_matrix[i].size(); j++)
			available[member_matrix[i][j]]+=member_matrix[i].size()-1;
	}
	
	//cout<<"available"<<endl;
	//prints(available);
	
	
	deque<int> available_nodes;
	for (int i=0; i<num_nodes; i++)
		available_nodes.push_back(i);
	
	
	deque<int> map_nodes;				// in the position i there is the new name of the node i
	for (int i=0; i<num_nodes; i++)
		map_nodes.push_back(0);
    
	
	for (int i=degree_seq_in.size()-1; i>=0; i--) {
		
		int & degree_here=internal_degree_seq_in[i];
		int try_this = irand(available_nodes.size()-1);
		
		int kr=0;
		while (internal_degree_seq_in[i] > available[available_nodes[try_this]]) {
            
			kr++;
			try_this = irand(available_nodes.size()-1);
			if(kr==3*num_nodes) {
                
				if(change_community_size(num_seq)==-1) {
					
					cerr<<"\n***********************\nERROR: this program needs more than one community to work fine"<<endl;
					return -1;
                    
				}
				
				cout<<"it took too long to decide the memberships; I will try to change the community sizes"<<endl;
                
				cout<<"new community sizes"<<endl;
				for (int i=0; i<num_seq.size(); i++)
					cout<<num_seq[i]<<" ";
				cout<<endl<<endl;
				
				return (internal_degree_and_membership(mixing_parameter, overlapping_nodes, max_mem_num, num_nodes, member_matrix, excess, defect, degree_seq_in, degree_seq_out, num_seq, internal_degree_seq_in, internal_degree_seq_out, fixed_range, nmin, nmax, tau2));
                
                
			}
			
			
		}
		
		
		
		map_nodes[available_nodes[try_this]]=i;
		
		available_nodes[try_this]=available_nodes[available_nodes.size()-1];
		available_nodes.pop_back();
		
        
        
	}
	
	
	for (int i=0; i<member_matrix.size(); i++) {
		for (int j=0; j<member_matrix[i].size(); j++)
			member_matrix[i][j]=map_nodes[member_matrix[i][j]];	
	}
	
	
	
	for (int i=0; i<member_matrix.size(); i++)
		sort(member_matrix[i].begin(), member_matrix[i].end());
    
    
	return 0;
    
}



int compute_internal_degree_per_node(int d, int m, deque<int> & a) {
	
	
	// d is the internal degree
	// m is the number of memebership 
	
	a.clear();
	int d_i= d/m;
	for (int i=0; i<m; i++)
		a.push_back(d_i);
    
	for(int i=0; i<d%m; i++)
		a[i]++;
	
	
	
    
	return 0;
    
}



/*
 int check_link_list(const deque<deque<int> > & link_list_in, const deque<int> & degree_seq_in) {
 
 
 for (int i=0; i<link_list_in.size(); i++) {
 
 int s=0;
 for (int j=0; j<link_list_in[i].size(); j++)
 s+=link_list_in[i][j];
 
 if(s!=degree_seq_in[i]) {
 
 int ok;
 cerr<<"wrong link list"<<endl;
 cin>>ok;
 
 }
 
 
 
 
 }
 
 
 
 
 }
 
 */


int build_subgraph(deque<set<int> > & Ein, deque<set<int> > & Eout, const deque<int> & nodes, const deque<int> & d_in, const deque<int> & d_out) {
	
	
	/*
     cout<<"nodes"<<endl;
     prints(nodes);
     
     cout<<"degrees"<<endl;
     prints(d_in);
     
     cout<<"d_out"<<endl;
     prints(d_out);
     //*/
	
	if(d_in.size()<3) {
		
		cerr<<"it seems that some communities should have only 2 nodes! This does not make much sense (in my opinion) Please change some parameters!"<<endl;
		return -1;
        
	}
	
	// this function is to build a network with the labels stored in nodes and the degree seq in degrees (correspondence is based on the vectorial index)
	// the only complication is that you don't want the nodes to have neighbors they already have
	
	
	
	// labels will be placed in the end
	deque<set<int> > en_in;			// this is the Ein of the subgraph
	deque<set<int> > en_out;		// this is the Eout of the subgraph
	
	
	{
    set<int> first;
    for(int i=0; i<nodes.size(); i++) {
        en_in.push_back(first);
        en_out.push_back(first);
    }
	}
	
	
	
	multimap <int, int> degree_node_out;
	deque<pair<int, int> > degree_node_in;
	
	for(int i=0; i<d_out.size(); i++)
		degree_node_out.insert(make_pair(d_out[i], i));
    
    
	deque<int> fakes;
	for(int i=0; i<d_in.size(); i++)
		fakes.push_back(i);
	
	shuffle_s(fakes);
	
    
	deque<int> antifakes(fakes.size());
	for(int i=0; i<d_in.size(); i++)
		antifakes[fakes[i]]=i;
	
	
	
	for(int i=0; i<d_in.size(); i++)
		degree_node_in.push_back(make_pair(d_in[i], fakes[i]));
	
    
	sort(degree_node_in.begin(), degree_node_in.end());
	
    
	for(int i=0; i<d_in.size(); i++)
		degree_node_in[i].second=antifakes[degree_node_in[i].second];
    
	
    
	
	
	deque<pair<int, int> >::iterator itlast = degree_node_in.end();
	
	/*
     for (int i=0; i<degree_node_in.size(); i++)
     cout<<degree_node_in[i].first<<" "<<degree_node_in[i].second<<endl;
     //*/
	
	deque<int> self_loop;
	
	int inserted=0;
	
	while (itlast != degree_node_in.begin()) {
		
		itlast--;
		
		
		multimap <int, int>::iterator itit= degree_node_out.end();
		deque <multimap<int, int>::iterator> erasenda;
		
		for (int i=0; i<itlast->first; i++) {
			
			if(itit!=degree_node_out.begin()) {
				
				itit--;
				
				if (itit->second!=itlast->second) {
					
					en_in[itlast->second].insert(itit->second);
					en_out[itit->second].insert(itlast->second);
					inserted++;
					
				}
				else
					self_loop.push_back(itlast->second);
				
                
				erasenda.push_back(itit);
				
			}
			
			else
				break;
            
		}
		
		
		//cout<<"degree node out before"<<endl;
		//prints(degree_node_out);
		
		for (int i=0; i<erasenda.size(); i++) {
			
			
			if(erasenda[i]->first>1)
				degree_node_out.insert(make_pair(erasenda[i]->first - 1, erasenda[i]->second));
            
			
			degree_node_out.erase(erasenda[i]);
            
			
            
		}
		
		//cout<<"degree node out after"<<endl;
		//prints(degree_node_out);
		
	}
	
	//cout<<inserted<<"<------ inserted"<<endl; 
	
	//cout<<"left "<<degree_node_out.size()<<endl;
	//cout<<"self loops "<<self_loop.size()<<endl;
    
    deque<int> degree_list_in;
    for(int kk=0; kk<d_in.size(); kk++)
        for(int k2=0; k2<d_in[kk]; k2++)
            degree_list_in.push_back(kk); 
    
    
	int not_done=0;
	
	for(int i=0; i<self_loop.size(); i++) {
        
		int node=self_loop[i];
        
		int stopper=d_in.size()*d_in.size();
		int stop=0;
		
		//cout<<"node "<<nodes[node]<<endl;
		
		bool breaker=false;
        
		while (stop++ < stopper) {
			
			
			while(true) {
				
				
				int random_mate=degree_list_in[irand(degree_list_in.size()-1)];
				if(random_mate==node || en_in[node].find(random_mate)!=en_in[node].end())
					break;
				
				deque <int> not_common;
				for (set<int>::iterator it_est=en_out[random_mate].begin(); it_est!=en_out[random_mate].end(); it_est++)
					if (en_out[node].find(*it_est)==en_out[node].end())
						not_common.push_back(*it_est);
                
                
				if (not_common.empty())
					break;
				
				int random_neigh=not_common[irand(not_common.size()-1)];
                
				
				en_out[node].insert(random_neigh);
				en_in[node].insert(random_mate);
				
				
				en_in[random_neigh].insert(node);
				en_in[random_neigh].erase(random_mate);
				
				en_out[random_mate].insert(node);
				en_out[random_mate].erase(random_neigh);
				
				breaker=true;
				break;
                
                
			}
			
			if(breaker)
				break;
			
            
		}
		
		if(!breaker)
			not_done++;
		
		
	}
	
	//cout<<"not done "<<not_done<<endl;
	
	// this is to randomize the subgraph -------------------------------------------------------------------
	
	for(int run=0; run<10; run++) for(int node_a=0; node_a<d_in.size(); node_a++) for(int krm=0; krm<en_out[node_a].size(); krm++) {
        
        
		int random_mate=degree_list_in[irand(degree_list_in.size()-1)];
		while (random_mate==node_a)
			random_mate=degree_list_in[irand(degree_list_in.size()-1)];
        
		
		if (en_out[node_a].find(random_mate)==en_out[node_a].end()) {
			
			deque <int> external_nodes;
			for (set<int>::iterator it_est=en_out[node_a].begin(); it_est!=en_out[node_a].end(); it_est++)
				external_nodes.push_back(*it_est);
            
            
			int	old_node=external_nodes[irand(external_nodes.size()-1)];
            
			
			deque <int> not_common;
			for (set<int>::iterator it_est=en_in[random_mate].begin(); it_est!=en_in[random_mate].end(); it_est++)
				if ((old_node!=(*it_est)) && (en_in[old_node].find(*it_est)==en_in[old_node].end()))
					not_common.push_back(*it_est);
            
			
			if (not_common.empty())
				break;
            
			int node_h=not_common[irand(not_common.size()-1)];
			
			
			en_out[node_a].insert(random_mate);
			en_out[node_a].erase(old_node);
			
			en_in[old_node].insert(node_h);
			en_in[old_node].erase(node_a);
			
			en_in[random_mate].insert(node_a);
			en_in[random_mate].erase(node_h);
			
			en_out[node_h].erase(random_mate);
			en_out[node_h].insert(old_node);
			
            
		}
        
        
	}
    
	
	
	// now I try to insert the new links into the already done network. If some multiple links come out, I try to rewire them
	
	deque < pair<int, int> > multiple_edge;
	for (int i=0; i<en_in.size(); i++) {
		
		for(set<int>::iterator its=en_in[i].begin(); its!=en_in[i].end(); its++) {
            
			bool already = !(Ein[nodes[i]].insert(nodes[*its]).second) ;		// true is the insertion didn't take place
			if (already)
				multiple_edge.push_back(make_pair(nodes[i], nodes[*its]));			
			else
				Eout[nodes[*its]].insert(nodes[i]);
            
		}
        
        
	}
	
	
	//cout<<"multiple "<<multiple_edge.size()<<endl;
	
	for (int i=0; i<multiple_edge.size(); i++) {
		
		
		int &a = multiple_edge[i].first;
		int &b = multiple_edge[i].second;
		
        
		// now, I'll try to rewire this multiple link among the nodes stored in nodes.
		int stopper_ml=0;
		
		while (true) {
            
			stopper_ml++;
			
			int random_mate=nodes[degree_list_in[irand(degree_list_in.size()-1)]];
			while (random_mate==a || random_mate==b)
				random_mate=nodes[degree_list_in[irand(degree_list_in.size()-1)]];
			
			if(Ein[a].find(random_mate)==Ein[a].end()) {
				
				deque <int> not_common;
				for (set<int>::iterator it_est=Eout[random_mate].begin(); it_est!=Eout[random_mate].end(); it_est++)
					if ((b!=(*it_est)) && (Eout[b].find(*it_est)==Eout[b].end()) && (binary_search(nodes.begin(), nodes.end(), *it_est)))
						not_common.push_back(*it_est);
				
				if(not_common.size()>0) {
                    
					int node_h=not_common[irand(not_common.size()-1)];
					
					
					
					Eout[random_mate].insert(a);
					Eout[random_mate].erase(node_h);
					
					Ein[node_h].erase(random_mate);
					Ein[node_h].insert(b);
					
					Eout[b].insert(node_h);
					Ein[a].insert(random_mate);
					
					break;
                    
                    
                    
				}
                
			}
			
			if(stopper_ml==2*Ein.size()) {
                
				cout<<"sorry, I need to change the degree distribution a little bit (one less link)"<<endl;
				break;
                
			}
			
			
			
		}
        
        
	}
	
	
    
	
	
	return 0;
    
}





int build_subgraphs(deque<set<int> > & Ein, deque<set<int> > & Eout, const deque<deque<int> > & member_matrix, deque<deque<int> > & member_list, deque<deque<int> > & link_list_in, deque<deque<int> > & link_list_out, 
                    const deque<int> & internal_degree_seq_in, const deque<int> & degree_seq_in, const deque<int> & internal_degree_seq_out, const deque<int> & degree_seq_out, const bool excess, const bool defect) {
	
	
	
	Ein.clear();
	Eout.clear();
	member_list.clear();
	link_list_in.clear();
	link_list_out.clear();
	
	int num_nodes=degree_seq_in.size();
	
	
	
	{
    
    deque<int> first;
    for (int i=0; i<num_nodes; i++)
        member_list.push_back(first);
	
	}
	
	
	
	for (int i=0; i<member_matrix.size(); i++)
		for (int j=0; j<member_matrix[i].size(); j++)
			member_list[member_matrix[i][j]].push_back(i);
	
    
	for (int i=0; i<member_list.size(); i++) {
		
		deque<int> liin;
		deque<int> liout;
        
		
		for (int j=0; j<member_list[i].size(); j++) {
			
			compute_internal_degree_per_node(internal_degree_seq_in[i], member_list[i].size(), liin);
			liin.push_back(degree_seq_in[i] - internal_degree_seq_in[i]);
			compute_internal_degree_per_node(internal_degree_seq_out[i], member_list[i].size(), liout);
			liout.push_back(degree_seq_out[i] - internal_degree_seq_out[i]);
            
            
		}
		
		link_list_in.push_back(liin);
		link_list_out.push_back(liout);
		
	}
	
	
	/*
     cout<<"link list in out ************************"<<endl;
     printm(link_list_in);
     printm(link_list_out);
     cout<<"link list in out ************************"<<endl;
     */
	
	// ------------------------ this is done to check if the sums of the internal degrees (in and out) are equal. if not, the program will change it in such a way to assure that. 
	
	
    
	for (int i=0; i<member_matrix.size(); i++) {
        
		
		int internal_cluster_in=0;
		int internal_cluster_out=0;
		
		
		for (int j=0; j<member_matrix[i].size(); j++) {
			
			int right_index= lower_bound(member_list[member_matrix[i][j]].begin(), member_list[member_matrix[i][j]].end(), i) - member_list[member_matrix[i][j]].begin();
			internal_cluster_in+=link_list_in[member_matrix[i][j]][right_index];
			internal_cluster_out+=link_list_out[member_matrix[i][j]][right_index];
			
            
		}
		
		//cout<<"internal_cluster difference "<<internal_cluster_in - internal_cluster_out<<" for nodes: "<<member_matrix[i].size()<<endl;
		
		
		int initial_diff= abs(internal_cluster_in - internal_cluster_out);
		for(int diffloop=0; diffloop<3*initial_diff; diffloop++) {
			
			
			if((internal_cluster_in - internal_cluster_out)==0)
				break;
			
            
			
            
			// if this does not work in a reasonable time the degree sequence will be changed
            
			for (int j=0; j<member_matrix[i].size(); j++) {		
				
				
				
				int random_mate=member_matrix[i][irand(member_matrix[i].size()-1)];
				int right_index= lower_bound(member_list[random_mate].begin(), member_list[random_mate].end(), i) - member_list[random_mate].begin();
				
				if(internal_cluster_in>internal_cluster_out) {
					
					if ((link_list_out[random_mate][right_index]<member_matrix[i].size()-1) && (link_list_out[random_mate][link_list_out[random_mate].size()-1] > 0 )) {
                        
						link_list_out[random_mate][right_index]++;
						link_list_out[random_mate][link_list_out[random_mate].size()-1]--;
						internal_cluster_out++;
						
						break;
					}
				}
				
				else if (link_list_out[random_mate][right_index] > 0) {
					
					link_list_out[random_mate][right_index]--;
					link_list_out[random_mate][link_list_out[random_mate].size()-1]++;
					internal_cluster_out--;
                    
					break;
                    
				}
                
			}			
            
		}
        
        
		//cout<<"internal_cluster difference after "<<internal_cluster_in - internal_cluster_out<<endl;
		
		for(int diffloop=0; diffloop<3*initial_diff; diffloop++) {
			
			
			if((internal_cluster_in - internal_cluster_out)==0)
				break;
			
            
			
            
			// if this does not work in a reasonable time the degree sequence will be changed
            
			for (int j=0; j<member_matrix[i].size(); j++) {		
				
				
				
				int random_mate=member_matrix[i][irand(member_matrix[i].size()-1)];
				int right_index= lower_bound(member_list[random_mate].begin(), member_list[random_mate].end(), i) - member_list[random_mate].begin();
				
				if(internal_cluster_in>internal_cluster_out) {
					
					if ((link_list_out[random_mate][right_index]<member_matrix[i].size()-1)) {
                        
						link_list_out[random_mate][right_index]++;
						internal_cluster_out++;
						
						break;
					}
				}
				
				else {
					
					link_list_out[random_mate][right_index]--;
					internal_cluster_out--;
                    
					break;
                    
				}
                
			}			
            
		}
		
		
		
		//cout<<"internal_cluster difference after after "<<internal_cluster_in - internal_cluster_out<<endl;
        
	}
	
	
	// ------------------------ this is done to check if the sums of the internal degrees (in and out) are equal. if not, the program will change it in such a way to assure that. 
	
	
    
	{
	
    set<int> first;
    for(int i=0; i<num_nodes; i++) {
        Ein.push_back(first);
        Eout.push_back(first);
        
    }
	
	}
	
	for (int i=0; i<member_matrix.size(); i++) {
		
		
		deque<int> internal_degree_in;
		deque<int> internal_degree_out;
        
		for (int j=0; j<member_matrix[i].size(); j++) {
            
			int right_index= lower_bound(member_list[member_matrix[i][j]].begin(), member_list[member_matrix[i][j]].end(), i) - member_list[member_matrix[i][j]].begin();
			internal_degree_in.push_back(link_list_in[member_matrix[i][j]][right_index]);
			internal_degree_out.push_back(link_list_out[member_matrix[i][j]][right_index]);
            
		}		
		
        
		
		if(build_subgraph(Ein, Eout, member_matrix[i], internal_degree_in, internal_degree_out)==-1)
			return -1;
        
        
	}
    
    
    
    
	return 0;
	
}


bool they_are_mate(int a, int b, const deque<deque<int> > & member_list) {
    
    
	for(int i=0; i<member_list[a].size(); i++) {
		
		if(binary_search(member_list[b].begin(), member_list[b].end(), member_list[a][i]))
			return true;
        
	}
    
	return false;
    
}


int compute_var_mate(deque<set<int> > & en_in,  const deque<deque<int> > & member_list) {
    
    
    
	int var_mate=0;
	for(int i=0; i<en_in.size(); i++) for(set<int>::iterator itss= en_in[i].begin(); itss!=en_in[i].end(); itss++) if(they_are_mate(i, *itss, member_list)) {
		var_mate++;
	}
    
    
    
	return var_mate;
}

int connect_all_the_parts(deque<set<int> > & Ein, deque<set<int> > & Eout, const deque<deque<int> > & member_list, const deque<deque<int> > & link_list_in, const deque<deque<int> > & link_list_out) {
    
	
	deque<int> d_in;
	for(int i=0; i<link_list_in.size(); i++)
		d_in.push_back(link_list_in[i][link_list_in[i].size()-1]);
	
	
	deque<int> d_out;
	for(int i=0; i<link_list_out.size(); i++)
		d_out.push_back(link_list_out[i][link_list_out[i].size()-1]);
    
	/*
     prints(d_in);
     prints(d_out);
     */
    
	
	deque<set<int> > en_in;			// this is the Ein of the subgraph
	deque<set<int> > en_out;		// this is the Eout of the subgraph
	
	
	{
    set<int> first;
    for(int i=0; i<member_list.size(); i++) {
        en_in.push_back(first);
        en_out.push_back(first);
    }
	}
	
	
	
	multimap <int, int> degree_node_out;
	deque<pair<int, int> > degree_node_in;
	
	for(int i=0; i<d_out.size(); i++)
		degree_node_out.insert(make_pair(d_out[i], i));
	
	deque<int> fakes;
	for(int i=0; i<d_in.size(); i++)
		fakes.push_back(i);
	
	shuffle_s(fakes);
	
	//prints(fakes);
	deque<int> antifakes(fakes.size());
	for(int i=0; i<d_in.size(); i++)
		antifakes[fakes[i]]=i;
	
	
	
	for(int i=0; i<d_in.size(); i++)
		degree_node_in.push_back(make_pair(d_in[i], fakes[i]));
	
	//printm(degree_node_in);
    
	sort(degree_node_in.begin(), degree_node_in.end());
	
	//printm(degree_node_in);
    
	for(int i=0; i<d_in.size(); i++)
		degree_node_in[i].second=antifakes[degree_node_in[i].second];
	
	/*
     prints(d_in);
     printm(degree_node_in);
     */
	
	deque<pair<int, int> >::iterator itlast = degree_node_in.end();
	
	deque<int> self_loop;
	
	
	//cout<<"difference in connect_all_parts "<<deque_int_sum(d_in) - deque_int_sum(d_out)<<endl;
	while (itlast != degree_node_in.begin()) {
		
		itlast--;
		
		
		multimap <int, int>::iterator itit= degree_node_out.end();
		deque <multimap<int, int>::iterator> erasenda;
		
		
		for (int i=0; i<itlast->first; i++) {
			
			if(itit!=degree_node_out.begin()) {
				
				itit--;
				
				if (itit->second!=itlast->second) {
					
					en_in[itlast->second].insert(itit->second);
					en_out[itit->second].insert(itlast->second);
                    
				}
				else
					self_loop.push_back(itlast->second);
				
                
				erasenda.push_back(itit);
				
			}
			
			else
				break;
            
		}
		
		
		for (int i=0; i<erasenda.size(); i++) {
			
			
			if(erasenda[i]->first>1)
				degree_node_out.insert(make_pair(erasenda[i]->first - 1, erasenda[i]->second));
            
			
			degree_node_out.erase(erasenda[i]);
            
			
            
		}
        
		
		
	}
	
	//cout<<"left "<<degree_node_out.size()<<endl;
	//cout<<"self loops "<<self_loop.size()<<endl;
    
    
    deque<int> degree_list_in;
    for(int kk=0; kk<d_in.size(); kk++)
        for(int k2=0; k2<d_in[kk]; k2++)
            degree_list_in.push_back(kk); 
    
    
	for(int i=0; i<self_loop.size(); i++) {
        
		int node=self_loop[i];
        
		int stopper=d_in.size()*d_in.size();
		int stop=0;
		
		//cout<<"node "<<node<<endl;
		
		bool breaker=false;
        
		while (stop++ < stopper) {
            
			//cout<<stop<<" "<<node<<endl;
			
			while(true) {
				
				
				int random_mate=degree_list_in[irand(degree_list_in.size()-1)];
				if(random_mate==node || en_in[node].find(random_mate)!=en_in[node].end())
					break;
				
				deque <int> not_common;
				for (set<int>::iterator it_est=en_out[random_mate].begin(); it_est!=en_out[random_mate].end(); it_est++)
					if (en_out[node].find(*it_est)==en_out[node].end())
						not_common.push_back(*it_est);
                
				if (not_common.empty())
					break;
				
                
				
				int random_neigh=not_common[irand(not_common.size()-1)];
                
				
				en_out[node].insert(random_neigh);
				en_in[node].insert(random_mate);
				
				
				en_in[random_neigh].insert(node);
				en_in[random_neigh].erase(random_mate);
				
				en_out[random_mate].insert(node);
				en_out[random_mate].erase(random_neigh);
				
				breaker=true;
				break;
                
                
			}
			
			if(breaker)
				break;
			
            
		}
		
		
		
        
        
	}
    
	
	// this is to randomize the subgraph -------------------------------------------------------------------
    
	
	for(int run=0; run<10; run++) for(int node_a=0; node_a<d_in.size(); node_a++) for(int krm=0; krm<en_out[node_a].size(); krm++) {
        
        
		int random_mate=degree_list_in[irand(degree_list_in.size()-1)];
		while (random_mate==node_a)
			random_mate=degree_list_in[irand(degree_list_in.size()-1)];
        
		
		if (en_out[node_a].find(random_mate)==en_out[node_a].end()) {
			
			deque <int> external_nodes;
			for (set<int>::iterator it_est=en_out[node_a].begin(); it_est!=en_out[node_a].end(); it_est++)
				external_nodes.push_back(*it_est);
            
            
			int	old_node=external_nodes[irand(external_nodes.size()-1)];
            
			
			deque <int> not_common;
			for (set<int>::iterator it_est=en_in[random_mate].begin(); it_est!=en_in[random_mate].end(); it_est++)
				if ((old_node!=(*it_est)) && (en_in[old_node].find(*it_est)==en_in[old_node].end()))
					not_common.push_back(*it_est);
            
			
			if (not_common.empty())
				break;
            
			int node_h=not_common[irand(not_common.size()-1)];
			
			
			en_out[node_a].insert(random_mate);
			en_out[node_a].erase(old_node);
			
			en_in[old_node].insert(node_h);
			en_in[old_node].erase(node_a);
			
			en_in[random_mate].insert(node_a);
			en_in[random_mate].erase(node_h);
			
			en_out[node_h].erase(random_mate);
			en_out[node_h].insert(old_node);
			
            
		}
        
        
	}
    
	
	
	// now there is a rewiring process to avoid "mate nodes" (nodes with al least one membership in common) to link each other
	
	int var_mate= compute_var_mate(en_in, member_list);	
	//cout<<"var mate = "<<var_mate<<endl;
	
	int stopper_mate=0;
	int mate_trooper=10;
	
	while(var_mate>0) {
        
		
		//cout<<"var mate = "<<var_mate<<endl;
        
		
		int best_var_mate=var_mate;
        
		// ************************************************  rewiring
		
		
		for(int a=0; a<d_in.size(); a++) for(set<int>::iterator its= en_in[a].begin(); its!=en_in[a].end(); its++) if(they_are_mate(a, *its, member_list)) {
            
			
			
			int b=*its;
			int stopper_m=0;
			
			while (true) {
                
				stopper_m++;
				
				int random_mate = degree_list_in[irand(degree_list_in.size()-1)];
				while (random_mate==a || random_mate==b)
					random_mate = degree_list_in[irand(degree_list_in.size()-1)];
				
				
				if(!(they_are_mate(a, random_mate, member_list)) && (en_in[a].find(random_mate)==en_in[a].end())) {
					
					deque <int> not_common;
					for (set<int>::iterator it_est=en_out[random_mate].begin(); it_est!=en_out[random_mate].end(); it_est++)
						if ((b!=(*it_est)) && (en_out[b].find(*it_est)==en_out[b].end()))
							not_common.push_back(*it_est);
					
					if(not_common.size()>0) {
                        
						int node_h=not_common[irand(not_common.size()-1)];
						
						
						en_out[random_mate].erase(node_h);
						en_out[random_mate].insert(a);
						
						en_in[node_h].erase(random_mate);
						en_in[node_h].insert(b);
						
						en_out[b].erase(a);
						en_out[b].insert(node_h);
						
						en_in[a].insert(random_mate);
						en_in[a].erase(b);
						
                        
						
						if(!they_are_mate(b, node_h, member_list))
							var_mate--;
						
						
						if(they_are_mate(random_mate, node_h, member_list))
							var_mate--;
						
						break;
                        
                        
                        
					}
                    
				}
				
				if(stopper_m==en_in[a].size())
					break;
				
				
				
			}
            
			
			break;		// this break is done because if you erased some link you have to stop this loop (en[i] changed)
            
            
		}
        
		// ************************************************  rewiring
		
		
        
        
		if(var_mate==best_var_mate) {
			
			stopper_mate++;
			
			if(stopper_mate==mate_trooper)
				break;
            
		}
		else
			stopper_mate=0;
		
		
		
		//cout<<"var mate = "<<var_mate<<endl;
        
        
	}
	
	
	
	//cout<<"var mate = "<<var_mate<<endl;
    
	for (int i=0; i<en_in.size(); i++) {
		
		for(set<int>::iterator its=en_in[i].begin(); its!=en_in[i].end(); its++) {
            
			Ein[i].insert(*its);
			Eout[*its].insert(i);
			
            
		}
        
        
	}
	
	
	
	return 0;
    
}

int internal_kin(deque<set<int> > & Ein, const deque<deque<int> > & member_list, int i) {
	
	int var_mate2=0;
	for(set<int>::iterator itss= Ein[i].begin(); itss!=Ein[i].end(); itss++) if(they_are_mate(i, *itss, member_list)) 
		var_mate2++;	
    
	return var_mate2;
	
}




int internal_kin_only_one(set<int> & Ein, const deque<int> & member_matrix_j) {		// return the overlap between Ein and member_matrix_j
	
	int var_mate2=0;
	
	for(set<int>::iterator itss= Ein.begin(); itss!=Ein.end(); itss++) {
        
		if(binary_search(member_matrix_j.begin(), member_matrix_j.end(), *itss))
			var_mate2++;
        
	}
	
	return var_mate2;
	
}

int erase_links(deque<set<int> > & Ein, deque<set<int> > & Eout, const deque<deque<int> > & member_list, const bool excess, const bool defect, const double mixing_parameter) {
    
	
	int num_nodes= member_list.size();
	
	int eras_add_times=0;
	
	if (excess) {
		
		for (int i=0; i<num_nodes; i++) {
			
			
			while ( (Ein[i].size()>1) &&  double(internal_kin(Ein, member_list, i))/Ein[i].size() < 1 - mixing_parameter) {
                
                //---------------------------------------------------------------------------------
				
				
				cout<<"degree sequence changed to respect the option -sup ... "<<++eras_add_times<<endl;
				
				deque<int> deqar;
				for (set<int>::iterator it_est=Ein[i].begin(); it_est!=Ein[i].end(); it_est++)
					if (!they_are_mate(i, *it_est, member_list))
						deqar.push_back(*it_est);
				
				
				if(deqar.size()==Ein[i].size()) {	// this shouldn't happen...
                    
					cerr<<"sorry, something went wrong: there is a node which does not respect the constraints. (option -sup)"<<endl;
					return -1;
                    
				}
				
				int random_mate=deqar[irand(deqar.size()-1)];
				
				Ein[i].erase(random_mate);
				Eout[random_mate].erase(i);
				
                
			}
		}
        
	}
	
	
	
	if (defect) {
        
		for (int i=0; i<num_nodes; i++)
			while ( (Ein[i].size()<Ein.size()) &&  double(internal_kin(Ein, member_list, i))/Ein[i].size() > 1 - mixing_parameter) {
				
				//---------------------------------------------------------------------------------
                
				
				cout<<"degree sequence changed to respect the option -inf ... "<<++eras_add_times<<endl;
                
                
				int stopper_here=num_nodes;
				int stopper_=0;
				
				int random_mate=irand(num_nodes-1);
				while ( (    (they_are_mate(i, random_mate, member_list)) || Ein[i].find(random_mate)!=Ein[i].end())      &&      (stopper_<stopper_here) ) {
					
					random_mate=irand(num_nodes-1);
					stopper_++;
                    
                    
				}
				
				if(stopper_==stopper_here) {	// this shouldn't happen...
                    
					cerr<<"sorry, something went wrong: there is a node which does not respect the constraints. (option -inf)"<<endl;
					return -1;
                    
				}
				
				
				
				Ein[i].insert(random_mate);
				Eout[random_mate].insert(i);
				
                
                
			}
        
		
	}
    
	//------------------------------------ Erasing links   ------------------------------------------------------
    
	
    
    
	return 0;
	
}