#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <unordered_set>
#include <stack>
using namespace std;
//CLASA GRAPH DE BAZA
class Graph{
//DATELE MEMBRE
protected:
int m_number_of_nodes;
//numarul de noduri
//METODELE
public:
//functia de citire virtuala -> implementata diferit in fiecare dintre clase
virtual void read_graph(char *file);
//parcurgerea in latime
virtual vector<int> BFS(int node);
//parcurgerea in adancime
virtual void DFS(int node, vector<int>& visited);
};
//METODE PUBLICE
void Graph::read_graph(char *file) {
return;
}
vector<int> Graph::BFS(int node){
vector<int> aux;
return aux;
}
void Graph::DFS(int node, vector<int> &visited) {
return;
}
//CLASA UNORIENTED GRAPH
class Unoriented_graph:protected Graph{
protected:
vector< vector<int> > m_adjancency_list;
public:
//citirea grafului
void read_graph(char *file);
//parcurgerea in adancime DFS
void DFS(int node, vector<int>& visited);
//numararea componentelor conexe
int number_of_connected_components();
//returnarea unui vector cu componentele conexe
vector< unordered_set<int> > generate_biconnected_components();
//gasirea muchiilor critice
vector< vector<int> > find_critical_edges();
private:
void DFSBiconnected(int current_node, int prec, int step, vector<int>& arrival_values, vector<int>& low_link_values,vector<unordered_set<int>>& biconnected_components,stack<pair <int, int>>& current_biconnected_components);
void DFSCriticals(int current_node, int& step, vector<int>& visited, vector<int>& prec, vector<int>& low_link_values, vector<int>& arrival_times, vector< vector<int> >& critical_edges);
};
//METODE PUBLICE GRAFURI NEORIENTATE
void Unoriented_graph::read_graph(char *file) {
ifstream f(file);
vector<int> aux;
int number_edges;
//citim numarul de noduri si numarul de muchii
f>>this->m_number_of_nodes >> number_edges;
//rezervam in matricea de vecini spatiu pentru numarul de noduri ale grafului
this->m_adjancency_list.assign(this->m_number_of_nodes + 1, aux);
//citim fiecare muchie si o marcam pentru ambele capete
for(int i = 0; i < number_edges; i++){
int x,y;
f >> x >> y;
this->m_adjancency_list[x].push_back(y);
this->m_adjancency_list[y].push_back(x);
}
}
void Unoriented_graph::DFS(int node, vector<int> &visited) {
//marcam nodul curent ca vizitat
visited[node] = 1;
//parcurgem vecinii si pentru fiecare vecin nevizitat aplicam recursiv DFS
for(int i = 0; i < this->m_adjancency_list[node].size(); i++){
if(visited[ this->m_adjancency_list[node][i] ] == 0){
DFS( this->m_adjancency_list[node][i], visited);
}
}
}
int Unoriented_graph::number_of_connected_components() {
//numarul componentelor conexe il vom tine in nr
int number = 0;
//initial toate nodurile sunt nevizitate
vector<int> visited;
visited.assign(m_number_of_nodes + 1, 0);
//pentru fiecare node nevizitat parcurgem din copil in copil prin DFS; de fiecare data cand dam de un node nevizitat inseamna ca avem o noua componenta conexa
for(int node = 1; node <= this->m_number_of_nodes; node++){
if(visited[node] == 0){
number++;
DFS(node, visited);
}
}
return number;
}
vector< unordered_set<int> >Unoriented_graph::generate_biconnected_components(){
vector<unordered_set<int>> biconnected_components;
stack<pair <int, int>> current_biconnected_component;
vector<int> arrival_value;
vector<int> low_link_values;
//initializam timpii de sosire si nivelul cel mai de sus pentru fiecare node
arrival_value.assign(this->m_number_of_nodes + 1, -1);
low_link_values.resize(this->m_number_of_nodes + 1);
//facem DFS
DFSBiconnected(1,0,0,arrival_value,low_link_values,biconnected_components,current_biconnected_component);
return biconnected_components;
}
vector< vector<int> > Unoriented_graph::find_critical_edges() {
int current_arrival_time = 0;
vector< vector<int> > critical_edges;
vector<int> visited;
vector<int> prec;
vector<int> low_link_values;
vector<int> arrival_times;
visited.assign(m_number_of_nodes + 1, 0);
prec.resize(m_number_of_nodes + 1);
low_link_values.resize(m_number_of_nodes + 1);
arrival_times.assign(m_number_of_nodes + 1, -1);
for(int i = 1; i <= m_number_of_nodes; i++){
if(visited[i] == 0){
DFSCriticals(i, current_arrival_time, visited, prec, low_link_values, arrival_times, critical_edges);
}
}
return critical_edges;
}
//METODE PRIVATE GRAFURI NEORIENTATE
void Unoriented_graph::DFSBiconnected(int current_node, int prec, int step, vector<int>& arrival_values, vector<int>& low_link_values,vector<unordered_set<int>>& biconnected_components,stack<pair <int, int>>& current_biconnected_components){
//marcam ca vizitat nodul curent
arrival_values[current_node] = step;
//momentan nivelul minim de intoarcere e nivelul curent, adica pasul
low_link_values[current_node] = step;
//parcurgem vecinii nodului curent
for(int i = 0; i < this->m_adjancency_list[current_node].size(); i++){
int neighbor = this->m_adjancency_list[current_node][i];
if(neighbor != prec){
//verificam pe ce fel de muchie suntem
//daca vecinul curent a mai fost vizitat inseamna ca am dat de o muchie de intoarcere, altfel suntem pe o muchie in jos
if(arrival_values[neighbor] == -1){
//am dat de o noua muchie din componenta biconexa curenta, asa ca o adaugam in stiva
current_biconnected_components.push(make_pair(current_node, neighbor));
//apelam DFS pentru vecinul curent
DFSBiconnected(neighbor, current_node, step + 1,arrival_values,low_link_values,biconnected_components,current_biconnected_components);
//verificam daca atunci cand ne am dus mai departe in graf
// am dat de o muchie de intoarcere care ne duce mai sus decat ne ducea nodul acesta inainte
if(low_link_values[current_node] > low_link_values[neighbor]){
low_link_values[current_node] = low_link_values[neighbor];
}
//verificam daca am ajuns la finalul componentei biconexe
if(low_link_values[neighbor] >= arrival_values[current_node]){
//trebuie sa adaugam noua componenta biconexa in vectorul de componenete biconexe
//si sa golim stiva cu muchiile componentei biconexe curente
unordered_set<int> aux;
int aux1, aux2;
do{
aux1 = current_biconnected_components.top().first;
aux2 = current_biconnected_components.top().second;
aux.insert(aux1);
aux.insert(aux2);
current_biconnected_components.pop();
} while (aux1 != current_node || aux2 != neighbor);
biconnected_components.push_back(aux);
}
}else{
//avem o muchie de intoarcere, trebuie sa verificam daca nu cumva duce mai sus
if(low_link_values[current_node] > arrival_values[neighbor]){
low_link_values[current_node] = arrival_values[neighbor];
}
}
}
}
}
void Unoriented_graph::DFSCriticals(int current_node, int &step, vector<int> &visited, vector<int> &prec,
vector<int> &low_link_values, vector<int> &arrival_times,
vector<vector<int>> &critical_edges) {
//marcam nodul ca vizitat in vectorul visited, actualizam timpul lui de ajungere iar low link value momentan e fix timpul de ajungere
visited[current_node] = 1;
arrival_times[current_node] = step;
low_link_values[current_node] = step;
//crestem timpul de ajungere pentru urmatorul DFS
step++;
//parcurgem vecinii nodului
for(int i = 0; i < m_adjancency_list[current_node].size(); i++){
int neighbor = m_adjancency_list[current_node][i];
//pentru fiecare vecin nevizitat, ii actualizam precedentul ca fiind nodul ai carui vecini ii parcurgem si intram in parcurgerea vecinilor vecinului
if (visited[neighbor] == 0){
prec[neighbor] = current_node;
DFSCriticals(neighbor, step, visited, prec, low_link_values, arrival_times, critical_edges);
//la iesirea din DFS incercam sa minimizam low link value pentru nodul curent, in cazul in care vecinul poate ajunge la un node mai indepartat
if(low_link_values[current_node] > low_link_values[neighbor]){
low_link_values[current_node] = low_link_values[neighbor];
}
//in cazul in care este o muchie critica, o adaugam in vectorul de muchii critice
if (low_link_values[neighbor] > arrival_times[current_node]){
critical_edges.push_back({current_node, neighbor});
}
}
else{
//pentru fiecare vecin deja vizitat incercam sa minimzam low link value pentru nodul nostru
if (neighbor != prec[current_node]){
if(low_link_values[current_node] > arrival_times[neighbor]){
low_link_values[current_node] = arrival_times[neighbor];
}
}
}
}
}
//CLASA ORIENTED GRAPH
class Oriented_graph: protected Graph{
protected:
vector< vector<int> > m_adjancency_list;
public:
void read_graph(char *file);
int read_graph_with_starting_node(char *file);
vector<int> BFS(int source);
vector<vector<int>> create_strongly_connected_components();
void tarjan(int node,stack<int>& current_component_stack,vector<int>& is_in_stack,vector<int>& arrival_values, int& current_arrival_value, vector<int>& low_link_values, vector<vector<int>>& strongly_connected_components);
stack<int> topological_sort();
private:
void DFS_topological_sort(int node, stack<int>& sort, vector<int>& visited);
};
//METODE PUBLICE ORIENTED GRAPHS
//citirea grafului orientat (fara costuri)
void Oriented_graph::read_graph(char *file) {
ifstream f(file);
vector<int> aux;
int number_edges;
//citim numarul de noduri si numarul de muchii
f >> m_number_of_nodes >> number_edges;
//rezervam in matricea de vecini spatiu pentru numarul de noduri ale grafului
this->m_adjancency_list.assign(this->m_number_of_nodes + 1, aux);
//citim fiecare muchie si o adaugam in lista de adiacenta, prin adagarea vecinului nodului din care porneste muchia
for(int i = 0; i < number_edges; i++){
int x,y;
f>>x>>y;
this->m_adjancency_list[x].push_back(y);
}
}
//citirea grafului orientat (fara costuri) cu node de pornire
int Oriented_graph::read_graph_with_starting_node(char *file) {
ifstream f(file);
vector<int> aux;
int number_edges, source;
//citim numarul de noduri, numarul de muchii si nodul de pornire
f >> this->m_number_of_nodes >> number_edges >> source;
//reyervam spatiu in matricea de vecini pentru numarul de noduri ale grafului
this->m_adjancency_list.assign(this->m_number_of_nodes + 1, aux);
//parcurgem fiecare muchie si o adaugam in lista de adiacenta, prin adaugarea vecinului la nodul din care porneste muchia
for(int i=0; i<number_edges; i++){
int x,y;
f >> x >> y;
this->m_adjancency_list[x].push_back(y);
}
return source;
}
//BFS -> returneaza un vector in care pe pozitia i se afla numarul minim de arce ce trebuie parcurse de la sursa data pana la nodul i
vector<int> Oriented_graph::BFS(int source) {
//initializam vectorul de distances minime
vector<int> distances;
distances.assign(this->m_number_of_nodes + 1, 0);
int curent;
//in coada vom pune nodurile pe massura ce le parcurgem
queue<int> current_nodes;
//initial toate nodurile sunt nevizitate, asaa ca initializam visited[orice node] = 0
vector<int> visited;
visited.assign(this->m_number_of_nodes + 1, 0);
//adaugam nodul sursa in coada si il marcam ca si vizitat
current_nodes.push(source);
visited[source] = 1;
//actualizam vectorul de distances pentru nodul curent cu distanta pana la el, adica 1
distances[source] = distances[source] + 1;
//facem BFS-ul
while( !current_nodes.empty() ){
curent = current_nodes.front();
//parcurgem vecinii nodului curent si pe fiecare vecin nevizitat il adaugam in coada, ii actualizam distanta pana la el si il marcam ca si vizitat
for(int i=0; i < this->m_adjancency_list[curent].size(); i++){
if(visited[ this->m_adjancency_list[curent][i] ] == 0){
current_nodes.push(this->m_adjancency_list[curent][i] );
distances[ current_nodes.back() ] = distances[curent] + 1;
visited[ this->m_adjancency_list[curent][i] ] = 1;
}
}
//am terminat cu nodul curent, il scoatem din coada
current_nodes.pop();
}
for(int i = 1; i <= this->m_number_of_nodes; i++){
distances[i]--;
}
return distances;
}
vector< vector<int> >Oriented_graph::create_strongly_connected_components() {
vector<vector<int>> strongly_connected_components;
stack<int> current_component;
int current_arrival_time = 0;
vector<int> is_in_stack;
is_in_stack.assign(this->m_number_of_nodes + 1, 0);
vector<int> arrival_values;
arrival_values.assign(this->m_number_of_nodes + 1, -1);
vector<int> low_link_values;
low_link_values.resize(this->m_number_of_nodes + 1);
for(int i=1; i<=this->m_number_of_nodes; i++){
if(arrival_values[i] == -1){
tarjan(i, current_component, is_in_stack, arrival_values, current_arrival_time, low_link_values, strongly_connected_components);
}
}
return strongly_connected_components;
}
void Oriented_graph::tarjan(int node, stack<int> ¤t_component_stack, vector<int> &is_in_stack,
vector<int> &arrival_values, int ¤t_arrival_value, vector<int> &low_link_values,
vector<vector<int>> &strongly_connected_components) {
//adaugam nodul in componenta tare conexa curenta, adica in current_component_stack
current_component_stack.push(node);
//marcam nodul ca facand parte din componenta tare conexa curenta prin vectorul is_in_stack
is_in_stack[node] = 1;
//marcam nodul ca vizitat, atribuindu-i chiar timpul de ajungere
arrival_values[node] = current_arrival_value;
//valoarea low Link momentan este tot nivelul nodului curent
low_link_values[node] = current_arrival_value;
//marim timpul de ajungere pentru urmatorul step
current_arrival_value++;
//parcurgem vecinii nodului curent, facand un DFS
for(int i=0; i<this->m_adjancency_list[node].size(); i++){
int neighbor = this->m_adjancency_list[node][i];
//verificam daca vecinul curent nu a fost inca vizitat
if(arrival_values[neighbor] == -1){
//aplicam tarjan pe nodul curent
tarjan(neighbor, current_component_stack, is_in_stack, arrival_values, current_arrival_value, low_link_values, strongly_connected_components);
//la iesire incercam sa minimizam valoarea low link a nodului curent, daca vecinul la care suntem a facut in timpul tarjan-ului una mai mica
if(low_link_values[neighbor] < low_link_values[node]){
low_link_values[node] = low_link_values[neighbor];
}
}else{ //daca vecinul a fost deja vizitat
//verificam daca vizitarea s-a produs in cadrul componentei tare conexe curente
if(is_in_stack[neighbor] == 1){
//incercam sa minimizam valoarea low link a nodului curent, in cazul in care vecinul curent ajunge la un node mai indepartat decat valoarea noastra curenta
if(low_link_values[neighbor] < low_link_values[node]){
low_link_values[node] = low_link_values[neighbor];
}
}
}
}
//verificam daca nodul curent inchide o componenta tare conexa
if(arrival_values[node] == low_link_values[node]){
//trebuie sa mutam componenta tare conexa curenta din stiva in vectorul cu toate componentele tare conexe din graf
vector<int> aux;
int aux_node;
do{
aux_node = current_component_stack.top();
aux.push_back(aux_node);
current_component_stack.pop();
is_in_stack[aux_node] = 0;
}while(aux_node != node);
strongly_connected_components.push_back(aux);
}
}
stack<int> Oriented_graph::topological_sort() {
vector<int> visited;
stack<int> sort;
visited.assign(m_number_of_nodes + 1, 0);
for(int i = 1; i <= this->m_number_of_nodes; i++){
if(visited[i] == 0){
DFS_topological_sort(i, sort, visited);
}
}
return sort;
}
//METODE PRIVATE ORIENTED GRAPHS
void Oriented_graph::DFS_topological_sort(int node, stack<int> &sort, vector<int>& visited) {
visited[node] = 1;
for(int i = 0; i < this->m_adjancency_list[node].size(); i++){
int neighbor = this->m_adjancency_list[node][i];
if(visited[neighbor] == 0){
DFS_topological_sort(neighbor, sort, visited);
}
}
sort.push(node);
}
//CLASA UNORIENTED GRAPH WITH COSTS
class Unoriented_graph_with_costs:Unoriented_graph{
private:
vector< vector<int> > m_costs_matrix;
public:
void read_graph(char *file);
vector< pair<int,int> > prim(int &cost_APM);
int get_number_of_nodes();
private:
void introduce_in_APM(int node, vector<int>& distances, vector<int>& vec);
void introduce_in_min_heap(int node, vector<int>& heap, vector<int>& poz, vector<int> distances);
int extract_root_min_heap(vector<int>& heap,vector<int>& poz, vector<int> distances);
void pop(int index, vector<int>& heap, vector<int>& poz, vector<int>& distances);
void push(int index, vector<int>& heap, vector<int>& poz, vector<int>& distances);
};
//METODE PUBLICE UNORIENTED GRAPHS WITH COSTS
void Unoriented_graph_with_costs::read_graph(char *file) {
fstream f(file);
vector<int> aux;
int number_of_edges;
f>>this->m_number_of_nodes;
this->m_adjancency_list.assign(this->m_number_of_nodes + 1, aux);
aux.assign(this->m_number_of_nodes + 1, -1);
m_costs_matrix.assign(this->m_number_of_nodes + 1, aux);
f >> number_of_edges;
for(int i = 0; i < number_of_edges; i++){
int x,y,cost;
f >> x >> y >> cost;
m_adjancency_list[x].push_back(y);
m_adjancency_list[y].push_back(x);
m_costs_matrix[x][y] = cost;
m_costs_matrix[y][x] = cost;
}
}
vector<pair<int,int>> Unoriented_graph_with_costs::prim(int &cost_APM) {
vector<pair<int,int>> APM_edges;
vector<int> vec;
vector<int> poz;
vector<int> distances;
vector<int> heap;
distances.assign(this->m_number_of_nodes + 1, 200000200);
vec.assign(this->m_number_of_nodes + 1, 0);
poz.assign(this->m_number_of_nodes + 1, 0);
heap.push_back(0);
distances[1] = 0;
introduce_in_APM(1, distances, vec);
for(int i = 2; i <= this->m_number_of_nodes; i++){
introduce_in_min_heap(i, heap, poz, distances);
}
for(int i = 1; i < this->m_number_of_nodes; i++){
int rad;
rad = extract_root_min_heap(heap, poz, distances);
introduce_in_APM(rad, distances, vec);
cost_APM = cost_APM + distances[rad];
APM_edges.push_back(make_pair(rad,vec[rad]));
for(int j = 0; j < this->m_adjancency_list[rad].size(); j++){
int nod;
nod = this->m_adjancency_list[rad][j];
if(poz[nod]) pop(poz[nod], heap, poz, distances);
}
}
return APM_edges;
}
int Unoriented_graph_with_costs::get_number_of_nodes() {
return this->m_number_of_nodes;
}
//METODE PRIVATE UNORIENTED GRAPH WITH COSTS
void Unoriented_graph_with_costs::introduce_in_APM(int node, vector<int> &distances, vector<int> &vec) {
for(int i = 0; i < this->m_adjancency_list[node].size(); i++){
int neighbor, cost;
neighbor = this->m_adjancency_list[node][i];
cost = m_costs_matrix[node][neighbor];
distances[neighbor] = min(distances[neighbor], cost);
if(distances[neighbor] == cost) vec[neighbor] = node;
}
}
void Unoriented_graph_with_costs::introduce_in_min_heap(int node, vector<int> &heap, vector<int> &poz,
vector<int> distances) {
heap.push_back(node);
poz[node] = heap.size() - 1;
pop(heap.size() - 1, heap, poz, distances);
}
int Unoriented_graph_with_costs::extract_root_min_heap(vector<int> &heap, vector<int> &poz, vector<int> distances) {
int root;
root = heap[1];
swap(heap[1],heap[ heap.size() - 1 ]);
swap(poz[ heap[1] ], poz[ heap[ heap.size() - 1 ] ]);
heap.pop_back();
push(1, heap, poz, distances);
poz[root] = 0;
return root;
}
void Unoriented_graph_with_costs::pop(int index, vector<int> &heap, vector<int> &poz, vector<int> &distances) {
while(index > 1 && distances[heap[index]] < distances[heap[index / 2]]){
swap(heap[index], heap[index / 2]);
swap(poz[heap[index]], poz[heap[index / 2]]);
index = index / 2;
}
}
void Unoriented_graph_with_costs::push(int index, vector<int> &heap, vector<int> &poz, vector<int> &distances) {
while((index * 2 <= heap.size() - 1 && distances[heap[index]] > distances[heap[index * 2]]) ||
(index * 2 + 1 <= heap.size() - 1 && distances[heap[index]] > distances[heap[index * 2 + 1]])){
if(distances[heap[index * 2]] < distances[heap[index * 2 + 1]] || index * 2 + 1 > heap.size() - 1){
swap(heap[index], heap[index * 2]);
swap(poz[heap[index]], poz[heap[index * 2]]);
index = index * 2;
}else{
swap(heap[index], heap[index * 2 + 1]);
swap(poz[heap[index]], poz[heap[index * 2 + 1]]);
index = index * 2 + 1;
}
}
}
//CLASA ORIENTED GRAPH WITH COSTS
class Oriented_graph_with_costs:Oriented_graph{
private:
};
//CLASA RETELE DE TRANSPORT
class Flow_network:Oriented_graph{
private:
};
//CLASA MULTIGRAF
class Multigraph:Graph{
private:
};
//HELPERE
void print_vector(vector<int> v, char *file){
ofstream g(file);
vector<int>::iterator it;
for(it = v.begin() + 1; it != v.end(); it++){
g << *it <<" ";
}
}
void print_vector_of_unordered_sets(vector< unordered_set<int> > v, char *file){
ofstream g(file);
vector< unordered_set<int> >::iterator it;
unordered_set<int>::iterator it_u;
g << v.size() << "\n";
for(it = v.begin(); it != v.end(); it++){
for(it_u = it->begin(); it_u != it->end(); it_u++){
g << *it_u << " ";
}
g << "\n";
}
}
void print_vector_of_vectors(vector< vector<int> >v, char *file){
ofstream g(file);
vector< vector<int> >::iterator it;
vector<int>::iterator it_u;
g << v.size() << "\n";
for(it = v.begin(); it != v.end(); it++){
for(it_u = it->begin(); it_u != it->end(); it_u++){
g << *it_u << " ";
}
g << "\n";
}
}
void print_stack(stack<int> s, char *file){
ofstream g(file);
while(!s.empty()){
g << s.top() << " ";
s.pop();
}
}
int main() {
//BFS INFOARENA
/*Oriented_graph g;
int source;
vector<int> distances;
source = g.read_graph_with_starting_node("../bfs.in");
distances = g.BFS(source);
print_vector(distances, "../bfs.out");*/
//DFS INFOARENA
/*Unoriented_graph g;
ofstream out("../dfs.out");
int number;
g.read_graph("../dfs.in");
number = g.number_of_connected_components();
out << number;*/
//COMPONENTE BICONEXE INFOARENA
/*Unoriented_graph g;
vector< unordered_set<int> > biconnected_components;
g.read_graph("../biconex.in");
biconnected_components = g.generate_biconnected_components();
print_vector_of_unordered_sets(biconnected_components, "../biconex.out");*/
//CTC INFOARENA
/*Oriented_graph g;
vector< vector<int> > strongly_connected_components;
g.read_graph("../ctc.in");
strongly_connected_components = g.create_strongly_connected_components();
print_vector_of_vectors(strongly_connected_components, "../ctc.out");*/
//SORTARE TOPOLOGICA INFOARENA
/*Oriented_graph g;
stack<int> topological_sort;
g.read_graph("../sortaret.in");
topological_sort = g.topological_sort();
print_stack(topological_sort, "../sortaret.out");*/
//MUCHII CRITICE GRAF NEORIENTAT LEETCODE
/*Unoriented_graph g;
vector< vector<int> > critical_edges;
g.read_graph("../critice.in");
critical_edges = g.find_critical_edges();
print_vector_of_vectors(critical_edges, "../critice.out");*/
//APM INFOARENA - ALGORITMUL LUI PRIM
Unoriented_graph_with_costs g;
vector< pair<int, int> > apm;
ofstream out("../apm.out");
int cost_apm;
g.read_graph("../apm.in");
cost_apm = 0;
apm = g.prim(cost_apm);
out << cost_apm << "\n";
out<<g.get_number_of_nodes() - 1<<"\n";
for(int i = 0; i < apm.size() - 1; i++){
out<<apm[i].first<<" "<<apm[i].second<<"\n";
}
return 0;
}