#include<bits/stdc++.h>
using namespace std;
#define endl '\n'
using ll = long long;
using ld = long double;
#define pb push_back
#define sz size()
typedef pair<int, ll> pil;
const int maxn = 1e5 + 1;
const ll inf = 1e15;
vector<vector<pil>> graph(maxn);
vector<vector<int>> aux(maxn);
vector<int> inDegree(maxn);
struct comp{
bool operator() (pil a, pil b){
return a.second > b.second;
}
};
struct edge {
int u, v; ll w;
// Ordenar las aristas por el menor peso
bool operator<(const edge& that) const {
return w < that.w; // Cambiar '<' por '>' para hallar el Maximal Spanning Tree
}
};
// Complejidad O(m*log(n))
void dijkstra(int source, int n, vector<ll>& d, vector<int>& parent){
for(int i = 1; i <= n; i++){
d[i] = inf;
parent[i] = -1;
}
d[source] = 0;
priority_queue<pil, vector<pil>, comp> pq;
pq.push({source, 0});
while(!pq.empty()){
int u = pq.top().first; ll w1 = pq.top().second;
pq.pop();
if(d[u] < w1) continue;
for(pil edge : graph[u]){
int v = edge.first; ll w2 = edge.second;
if(d[v] > w1 + w2){
d[v] = w1 + w2;
parent[v] = u;
pq.push({v, d[v]});
}
}
}
}
void topoSort(int s, vector<int>& orden){
queue<int> q; q.push(s);
orden.pb(s);
while(!q.empty()){
int u = q.front(); q.pop();
for(int v : aux[u]){
inDegree[v]--;
if(!inDegree[v]){
q.push(v);
orden.pb(v);
}
}
}
}
void createAuxGraph(int s, int t, vector<ll>& ds, vector<ll>& dt, vector<edge>& edges, vector<bool>& vertexes){
for(edge e : edges){
int u = e.u, v = e.v; ll w = e.w;
if(ds[u] + w + dt[v] == ds[t]){
aux[u].pb(v);
inDegree[v]++;
vertexes[u] = 1; vertexes[v] = 1;
}
else if(ds[v] + w + dt[u] == ds[t]){
aux[v].pb(u);
inDegree[u]++;
vertexes[u] = 1; vertexes[v] = 1;
}
}
}
void solver(){
int n, m, s, t, u, v; cin>>n>>m>>s>>t>>u>>v;
vector<edge> edges;
for(int i = 0; i < m; i++){
int a, b; ll w;
cin>>a>>b>>w;
edges.pb({a, b, w});
graph[a].pb({b, w});
graph[b].pb({a, w});
}
vector<ll> ds(n+1), dt(n+1), du(n+1), dv(n+1);
vector<int> parentS(n+1), parentT(n+1), parentU(n+1), parentV(n+1);
dijkstra(s, n, ds, parentS);
dijkstra(t, n, dt, parentT);
dijkstra(u, n, du, parentU);
dijkstra(v, n, dv, parentV);
vector<bool> vertexes(n+1);
createAuxGraph(s, t, ds, dt, edges, vertexes);
vector<int> orden;
topoSort(s, orden);
vector<ll> dpU(n+1, inf);
for(int i = 0; i < orden.sz; i++){
int a = orden[i];
dpU[a] = du[a];
if(parentS[a] != -1 && vertexes[parentS[a]]) dpU[a] = min(dpU[a], dpU[parentS[a]]);
}
vector<ll> dpV(n+1, inf);
for(int i = 0; i < orden.sz; i++){
int a = orden[i];
dpV[a] = dv[a];
if(parentS[a] != -1 && vertexes[parentS[a]]) dpV[a] = min(dpV[a], dpV[parentS[a]]);
}
ll ans = du[v];
for(int i = 0; i < orden.sz; i++) ans = min(ans, dpU[orden[i]] + dpV[orden[i]]);
cout<<ans<<endl;
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(NULL);
int t = 1;
// cin>>t;
while(t--){
solver();
}
return 0;
}
