#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int lim = 1e5+5;
const ll inf = 1e18;
int n, m, S, T, U, V;
ll ans = inf;
//ARESTAS
struct Edge{ int a, b, c; };
vector<Edge> edges;
vector<int> adj[lim], weight[lim];
void addEdge(int a, int b, int c){
edges.push_back({a, b, c});
adj[a].push_back(b);
adj[b].push_back(a);
weight[a].push_back(c);
weight[b].push_back(c);
}
//DIJK FOR MIN_PATHS
ll d[4][lim];
void dijk(int r){
set<pair<ll, int>> can;
for(int i = 1; i <= n; i++) d[r][i] = inf;
if(r == 0) d[r][S] = 0;
else if(r == 1) d[r][T] = 0;
else if(r == 2) d[r][U] = 0;
else if(r == 3) d[r][V] = 0;
for(int i = 1; i <= n; i++) can.emplace(d[r][i], i);
while(!can.empty()){
int no = can.begin()->second;
can.erase(can.begin());
for(int i = 0; i < adj[no].size(); i++){
int v = adj[no][i], p = weight[no][i];
if(d[r][v] > d[r][no] + p){
can.erase({d[r][v], v});
d[r][v] = d[r][no] + p;
can.emplace(d[r][v], v);
}
}
}
}
//DAGs
vector<int> dag[2][lim];
ll dpU[2][lim], dpV[2][lim];
int ing[2][lim];
void solve(int r){
queue<int> can;
for(int i = 1; i <= n; i++){
if(ing[r][i] == 0) can.push(i);
}
while(!can.empty()){
int no = can.front();
can.pop();
dpU[r][no] = min(dpU[r][no], d[2][no]);
dpV[r][no] = min(dpV[r][no], d[3][no]);
if(dag[r][no].empty()) continue;
for(int v : dag[r][no]){
ing[r][v]--;
if(ing[r][v] == 0) can.push(v);
if(r == 0){
dpU[0][v] = min(dpU[0][v], dpU[0][no]);
dpV[1][v] = min(dpV[1][v], dpV[1][no]);
}
else{
dpU[1][v] = min(dpU[1][v], dpU[1][no]);
dpV[0][v] = min(dpV[0][v], dpV[0][no]);
}
}
}
}
int main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m;
cin >> S >> T >> U >> V;
for(int i = 1; i <= m; i++){
int a, b, c; cin >> a >> b >> c;
addEdge(a, b, c);
}
for(int i = 0; i < 4; i++) dijk(i);
for(Edge &e : edges){
if(d[0][e.a] + e.c + d[1][e.b] == d[0][T]){
dag[0][e.a].push_back(e.b); ing[0][e.b]++;
dag[1][e.b].push_back(e.a); ing[1][e.a]++;
}
if(d[0][e.b] + e.c + d[1][e.a] == d[0][T]){
dag[1][e.a].push_back(e.b); ing[1][e.b]++;
dag[0][e.b].push_back(e.a); ing[0][e.a]++;
}
}
for(int i = 1; i <= n; i++) dpU[0][i] = dpV[0][i] = dpU[1][i] = dpV[1][i] = inf;
solve(0);
solve(1);
ans = d[2][V];
for(int i = 1; i <= n; i++)
ans = min({ans, dpU[0][i]+dpV[0][i], dpU[1][i]+dpV[1][i]});
cout << ans << '\n';
}
