#include <bits/stdc++.h>
using namespace std;
// ifstream in("citire.in");
ifstream in("apm.in");
ofstream out("apm.out");
const int infinity = numeric_limits<int>::max();
const int infinitytMin = numeric_limits<int>::min();
// muchie de la x la y cu costul cost
struct Muchie
{
int x, y;
int cost = 0;
int capacitate = -1;
int flux = -1;
Muchie() = default;
Muchie(int x, int y, int cost)
{
this->x = x;
this->y = y;
this->cost = cost;
}
Muchie(int x, int y)
{
this->x = x;
this->y = y;
}
Muchie(int x, int y, int flux, int capacitate)
{
this->x = x;
this->y = y;
this->flux = flux;
this->capacitate = capacitate;
}
};
bool comparison(Muchie m1, Muchie m2)
{
return m1.cost < m2.cost;
}
// nodul x are in lista de adiacenta un Nod cu nod=y si costul = 10
// daca avem muchie de la x la y cu costul 10
struct Nod
{
int nod;
int cost = 0;
int capacitate = -1;
int flux = -1;
Nod() = default;
Nod(int nod) { this->nod = nod; }
Nod(int nod, int cost)
{
this->nod = nod;
this->cost = cost;
}
Nod(int nod, int flux, int capacitate)
{
this->nod = nod;
this->flux = flux;
this->capacitate = capacitate;
}
bool operator<(const Nod &obj) const
{
return this->cost > obj.cost; //> pt min-heap
}
};
class Graf
{
public:
int nrNoduri;
int nrMuchii;
vector<bool> vizitat;
vector<int> grad_intern;
vector<int> grad_extern;
vector<vector<Nod>> lista_adiacenta;
vector<Muchie> muchii;
Graf() = default;
Graf(int nrNoduri)
{
this->nrNoduri = nrNoduri;
vizitat.resize(nrNoduri + 1);
grad_intern.resize(nrNoduri + 1, 0);
grad_extern.resize(nrNoduri + 1, 0);
lista_adiacenta.resize(nrNoduri + 1);
}
Graf(int nrNoduri, int nrMuchii)
{
this->nrMuchii = nrMuchii;
this->nrNoduri = nrNoduri;
vizitat.resize(nrNoduri + 1);
grad_intern.resize(nrNoduri + 1, 0);
grad_extern.resize(nrNoduri + 1, 0);
lista_adiacenta.resize(nrNoduri + 1);
}
void calculeazaGrad()
{
for (int nod = 1; nod <= nrNoduri; nod++)
grad_extern[nod] = grad_intern[nod] = 0;
for (int nod = 1; nod <= nrNoduri; nod++)
{
for (auto vecin : lista_adiacenta[nod])
{
grad_intern[vecin.nod] += 1;
grad_extern[nod] += 1;
}
}
}
void dfs(int start, stack<int> &stiva)
{
vizitat[start] = true;
for (auto vecin : lista_adiacenta[start])
{
if (vizitat[vecin.nod] == false)
{
dfs(vecin.nod, stiva);
}
}
stiva.push(start);
}
void bfs(int start, vector<int> &tata)
{
queue<int> coada;
coada.push(start);
vizitat[start] = 1;
while (!coada.empty())
{
int nod = coada.front();
coada.pop();
for (auto vecin : lista_adiacenta[nod])
{
if (vizitat[vecin.nod] == 0)
{
coada.push(vecin.nod);
vizitat[vecin.nod] = 1;
tata[vecin.nod] = nod;
}
}
}
}
vector<int> sortareTopologica()
{
vector<int> noduri_start;
stack<int> stiva;
for (int nod = 1; nod <= nrNoduri; nod++)
{
if (grad_intern[nod] == 0)
{
noduri_start.push_back(nod);
}
}
for (auto nod : noduri_start)
{
dfs(nod, stiva);
}
vector<int> sortaretopologica;
while (!stiva.empty())
{
sortaretopologica.push_back(stiva.top());
stiva.pop();
}
return sortaretopologica;
}
void printGraf()
{
for (int i = 1; i <= nrNoduri; i++)
{
cout << i << ": ";
for (auto nod : lista_adiacenta[i])
cout << nod.nod << "(" << nod.cost << ") ";
cout << endl;
}
}
void printGrad()
{
for (int i = 1; i <= nrNoduri; i++)
{
cout << i << "-> grad intern = " << grad_intern[i] << ", grad extern = " << grad_extern[i] << endl;
}
}
// drumul de cost maxim pentru graf orientat/neorientat aciclic de sursa si final unic
// costul maxim = drum[end]
// drumul se obtine de la end pana ajungem la sursa prin vectorul de tati
void drumCritic(int sursa, vector<int> &drum, vector<int> &tata)
{
drum.resize(nrNoduri + 1);
tata.resize(nrNoduri + 1);
for (int i = 1; i <= nrNoduri; i++)
{
drum[i] = -1;
tata[i] = 0;
}
drum[sursa] = 0;
vector<int> top = sortareTopologica();
for (auto nod : top)
{
for (auto vecin : lista_adiacenta[nod])
{
if (drum[nod] + vecin.cost > drum[vecin.nod])
{
drum[vecin.nod] = drum[nod] + vecin.cost;
tata[vecin.nod] = nod;
}
}
}
}
void Djikstra(int sursa, vector<int> &drum, vector<int> &tata)
{
drum.clear();
tata.clear();
drum.resize(nrNoduri + 1);
tata.resize(nrNoduri + 1);
for (int i = 1; i <= nrNoduri; i++)
{
drum[i] = infinity;
tata[i] = 0;
}
drum[sursa] = 0;
auto cmp = [&](int nod1, int nod2)
{ return drum[nod1] > drum[nod2]; };
priority_queue<int, vector<int>, decltype(cmp)> pq(cmp);
// daca am adaugat o sursa imaginara si doresc sa pornesc din locuri multiple :
// for (int i = 1; i <= nrNoduri; i++)
// pq.push(i);
pq.push(sursa);
while (!pq.empty())
{
int nod = pq.top();
pq.pop();
for (auto vecin : lista_adiacenta[nod])
{
if (drum[nod] + vecin.cost < drum[vecin.nod])
{
drum[vecin.nod] = drum[nod] + vecin.cost;
pq.push(vecin.nod);
tata[vecin.nod] = nod;
}
}
}
}
// intoarce false daca contine circuit negativ, true daca nu
bool BellmanFord(int sursa, vector<int> &drum, vector<int> &tata, int &negativStart)
{
drum.resize(nrNoduri + 1);
tata.resize(nrNoduri + 1);
for (int i = 1; i <= nrNoduri; i++)
{
drum[i] = infinity;
tata[i] = 0;
}
drum[sursa] = 0;
for (int k = 1; k <= nrNoduri - 1; k++)
{
for (auto muchie : muchii)
{
if (drum[muchie.x] < infinity && drum[muchie.x] + muchie.cost < drum[muchie.y])
{
drum[muchie.y] = drum[muchie.x] + muchie.cost;
tata[muchie.y] = muchie.x;
}
}
}
// a n a rulare a algoritmului pentru a detecta ciclul negativ
for (auto muchie : muchii)
{
if (drum[muchie.x] < infinity && drum[muchie.x] + muchie.cost < drum[muchie.y])
{
drum[muchie.y] = drum[muchie.x] + muchie.cost;
tata[muchie.y] = muchie.x;
negativStart = muchie.y;
return false;
}
}
return true;
}
// BellmanFord cu queue -> mai rapid decat primul si da 100% pe toate cazurile pe infoarena
bool BellmanFordQueue(int sursa, vector<int> &drum, vector<int> &tata, int &negativStart)
{
drum.resize(nrNoduri + 1);
tata.resize(nrNoduri + 1);
for (int i = 1; i <= nrNoduri; i++)
{
drum[i] = infinity;
tata[i] = 0;
}
drum[sursa] = 0;
vector<bool> inQueue(nrNoduri + 1, false);
queue<int> q;
q.push(sursa);
inQueue[sursa] = true;
vector<int> lungime(nrNoduri + 1, 0);
while (!q.empty())
{
int nod = q.front();
q.pop();
inQueue[nod] = false;
for (auto vecin : lista_adiacenta[nod])
{
if (drum[nod] < infinity && drum[nod] + vecin.cost < drum[vecin.nod])
{
drum[vecin.nod] = drum[nod] + vecin.cost;
tata[vecin.nod] = nod;
if (inQueue[vecin.nod] == false)
{
q.push(vecin.nod);
inQueue[vecin.nod] = true;
}
lungime[vecin.nod] = lungime[nod] + 1;
if (lungime[vecin.nod] > nrNoduri - 1)
{
negativStart = vecin.nod;
return false;
}
}
}
}
return true;
}
void afisareDrum(int start, int end, vector<int> tata)
{
// cout << start << " " << end << endl;
// for (int i = 1; i <= nrNoduri; i++)
// cout << tata[i] << " ";
// cout << endl;
vector<int> drum;
if (start != end) // daca e circuit nu trebuie sa punem finalul de 2 ori
drum.push_back(end);
while (tata[end] != start)
{
end = tata[end];
drum.push_back(end);
}
drum.push_back(start);
for (int i = drum.size() - 1; i >= 0; i--)
cout << drum[i] << " ";
}
// daca dupa algoritm avem drumuri[i][i] < 0 pentru un i => circuit negativ
// am decis ca daca nu exista drum atunci in matrice e 0
// de asemenea drumuri[i][i] = lantul minim folosin cel putin un arc sau infinit daca nu exista un
// lant de lungime nevida de la i la i ( circuit practic )
void FloydWarshall(vector<vector<int>> &drumuri, vector<vector<int>> &predecesor)
{
drumuri.resize(nrNoduri + 1);
predecesor.resize(nrNoduri + 1);
for (int nod = 1; nod <= nrNoduri; nod++)
{
drumuri[nod].resize(nrNoduri + 1, infinity);
predecesor[nod].resize(nrNoduri + 1, 0);
for (auto vecin : lista_adiacenta[nod])
{
drumuri[nod][vecin.nod] = vecin.cost;
predecesor[nod][vecin.nod] = nod;
}
}
// for (int i = 1; i <= nrNoduri; i++)
// drumuri[i][i] = 0;
for (int k = 1; k <= nrNoduri; k++)
{
for (int i = 1; i <= nrNoduri; i++)
{
for (int j = 1; j <= nrNoduri; j++)
{
if (drumuri[i][k] < infinity && drumuri[k][j] < infinity)
{
if (drumuri[i][j] > drumuri[i][k] + drumuri[k][j])
{
drumuri[i][j] = drumuri[i][k] + drumuri[k][j];
predecesor[i][j] = predecesor[k][j];
}
}
}
}
}
for (int i = 1; i <= nrNoduri; i++)
{
for (int j = 1; j <= nrNoduri; j++)
{
if (drumuri[i][j] == infinity)
drumuri[i][j] = 0; // nu exista drum
}
}
}
void drumMat(int x, int y, vector<vector<int>> predecesor)
{
if (x != y)
drumMat(x, predecesor[x][y], predecesor);
cout << y << " ";
}
void afisCircuitMat(int x, int y, vector<vector<int>> predecesor)
{
if (predecesor[x][y] != x)
afisCircuitMat(x, predecesor[x][y], predecesor);
cout << y << " ";
}
void afisareDrumuriMat(vector<vector<int>> drumuri, vector<vector<int>> predecesor)
{
for (int i = 1; i <= nrNoduri; i++)
{
cout << i << ": \n";
for (int j = 1; j <= nrNoduri; j++)
{
cout << " " << j << ": ";
if (drumuri[i][j] == 0)
cout << "nu exista drum\n";
else
{
drumMat(i, j, predecesor);
cout << " cu costul: " << drumuri[i][j] << endl;
}
}
}
}
long long Prim(int start, vector<Muchie> &muchiiApcm)
{
vector<int> d(nrNoduri + 1, infinity);
vector<int> tata(nrNoduri + 1, -1);
vector<bool> inHeap(nrNoduri + 1, true);
auto cmp = [&](int nod1, int nod2)
{ return d[nod1] > d[nod2]; };
priority_queue<Nod> minHeap;
d[start] = 0;
minHeap.push(Nod(start, d[start]));
while (!minHeap.empty())
{
Nod u = minHeap.top();
minHeap.pop();
inHeap[u.nod] = false;
for (auto vecin : lista_adiacenta[u.nod])
{
if (inHeap[vecin.nod] && vecin.cost < d[vecin.nod])
{
d[vecin.nod] = vecin.cost;
tata[vecin.nod] = u.nod;
minHeap.push(Nod(vecin.nod, d[vecin.nod]));
}
}
}
long long cost = 0;
for (int i = 1; i <= nrNoduri; i++)
if (i != start)
{
muchiiApcm.push_back(Muchie(i, tata[i]));
cost += d[i];
}
return cost;
}
int Repr(int x, vector<int> &tata)
{
if (tata[x] == 0)
return x;
tata[x] = Repr(tata[x], tata);
return tata[x];
}
void Union(int x, int y, vector<int> &tata, vector<int> &h)
{
int rx, ry;
rx = Repr(x, tata);
ry = Repr(y, tata);
if (h[rx] > h[ry])
{
tata[ry] = rx;
}
else
{
tata[rx] = ry;
if (h[rx] == h[ry])
h[rx] = h[ry] + 1;
}
}
long long Kruskal(vector<Muchie> &apcm)
{
sort(muchii.begin(), muchii.end(), comparison);
vector<int> tata(nrNoduri + 1, 0), inaltime(nrNoduri + 1, 0);
int nrSelectii = 0;
long long costTotal = 0;
for (auto muchie : muchii)
{
if (Repr(muchie.x, tata) != Repr(muchie.y, tata))
{
apcm.push_back(muchie);
costTotal += muchie.cost;
Union(muchie.x, muchie.y, tata, inaltime);
nrSelectii += 1;
if (nrSelectii == nrNoduri - 1)
return costTotal;
}
}
}
};
void iterativeDFS(int start, vector<vector<int>> la, vector<int> &tati)
{
int n = la.size() - 1;
vector<bool> vizitat(n + 1, false);
stack<int> stack;
stack.push(start);
while (!stack.empty())
{
int nod = stack.top();
stack.pop();
if (vizitat[nod] == false)
{
cout << nod;
vizitat[nod] = true;
}
for (auto vecin : la[nod])
if (vizitat[vecin] == false)
stack.push(vecin);
}
}
int main()
{
int n, m;
in >> n >> m;
Graf g(n, m);
for (int i = 1; i <= m; i++)
{
int x, y, c;
in >> x >> y >> c;
g.lista_adiacenta[x].push_back(Nod(y, c));
g.lista_adiacenta[y].push_back(Nod(x, c));
g.muchii.push_back(Muchie(x, y, c));
}
vector<Muchie> muchiiApcm;
long long cost = g.Kruskal(muchiiApcm);
out << cost << "\n";
out << n - 1 << endl;
for (auto m : muchiiApcm)
out << m.x << " " << m.y << endl;
return 0;
}