#include <bits/stdc++.h>
#define DIM 100010
#define INF 2000000000000000000LL
using namespace std;
priority_queue <pair<long long,int>, vector<pair<long long,int> >, greater<pair<long long,int> > > H;
priority_queue <pair<long long,pair<int,int> >, vector<pair<long long,pair<int,int> > >, greater <pair<long long,pair<int,int> > > > c;
vector <pair<int,long long> > L[DIM];
vector <int> fth[DIM],edg[DIM];
long long dist_s[DIM],dist_u[DIM],dist_t[DIM],dp[DIM][5];
int viz[DIM];
int n,m,s,t,x,y,i,u,v;
long long cost;
void dfs (int nod){
viz[nod] = 1;
for (auto vecin : fth[nod])
if (!viz[vecin]){
edg[vecin].push_back(nod);
dfs (vecin);
}
}
void dijkstra (long long dp[], int start){
for (i=1;i<=n;i++)
dp[i] = INF;
dp[start] = 0;
while (!H.empty())
H.pop();
//H.clear();
H.push (make_pair(0,start));
while (!H.empty()){
int nod = H.top().second;
long long cost = H.top().first;
H.pop();
if (dp[nod] < cost)
continue;
for (auto it : L[nod]){
int vecin = it.first; long long new_cost = it.second;
if (dp[nod] + new_cost < dp[vecin]){
dp[vecin] = dp[nod] + new_cost;
H.push(make_pair(dp[vecin],vecin));
}}}}
int main (){
// ifstream cin ("date.in");
// ofstream cout ("date.out");
cin>>n>>m>>s>>t>>u>>v;
for (i=1;i<=m;i++){
cin>>x>>y>>cost;
L[x].push_back(make_pair(y,cost));
L[y].push_back(make_pair(x,cost));
}
for (i=1;i<=n;i++)
dist_s[i] = INF;
dist_s[s] = 0;
H.push(make_pair(0,s));
while (!H.empty()){
int nod = H.top().second;
long long cost = H.top().first;
H.pop();
if (dist_s[nod] < cost)
continue;
for (auto it : L[nod]){
int vecin = it.first; long long new_cost = it.second;
if (dist_s[nod] + new_cost < dist_s[vecin]){
dist_s[vecin] = dist_s[nod] + new_cost;
fth[vecin].clear();
fth[vecin].push_back(nod);
H.push(make_pair(dist_s[vecin],vecin));
} else {
if (dist_s[nod] + new_cost == dist_s[vecin])
fth[vecin].push_back(nod);
}}}
/// marchez toate nodurile care se afla pe drumurile minime de la S la T
viz[t] = 1;
dfs (t);
//dijkstra (dist_u,u);
//dijkstra (dist_v,v);
dijkstra (dist_t,t);
/// dp[nod][stare] - distanta minima de la u la un nod
/// 0 - nu am intrat pe un drum minim
/// 1 - merg pe un drum minim spre t
/// 2 - merg pe un drum minim spre s
/// 3 - am mers pe un drum minim, dar acum nu mai sunt
for (i=1;i<=n;i++)
dp[i][0] = dp[i][1] = dp[i][2] = dp[i][3] = INF;
dp[u][0] = 0;
c.push(make_pair(0,make_pair(u,0)));
if (viz[u]){
dp[u][1] = dp[u][2] = 0;
c.push(make_pair(0,make_pair(u,1)));
c.push(make_pair(0,make_pair(u,2)));
}
while (!c.empty()){
int nod = c.top().second.first;
int stare = c.top().second.second;
long long cost = c.top().first;
c.pop();
if (dp[nod][stare] < cost)
continue;
for (auto it : L[nod]){
int vecin = it.first; long long new_cost = it.second;
if (stare == 0){
if (dp[nod][stare] + new_cost < dp[vecin][stare]){
dp[vecin][stare] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][stare],make_pair(vecin,stare)));
}
if (viz[vecin]){ /// pot sa actualizez dp[vecin][1/2]
if (dp[nod][stare] + new_cost < dp[vecin][1]){
dp[vecin][1] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][1],make_pair(vecin,1)));
}
if (dp[nod][stare] + new_cost < dp[vecin][2]){
dp[vecin][2] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][2],make_pair(vecin,2)));
}}
} else {
if (stare == 1){
if (dist_s[vecin] + new_cost + dist_t[nod] == dist_s[t]){ /// pot sa pastrez starea asta
if (dp[nod][stare] < dp[vecin][stare]){
dp[vecin][stare] = dp[nod][stare];
c.push(make_pair(dp[vecin][stare],make_pair(vecin,stare)));
}
}
/// trec in starea 3
if (dp[nod][stare] + new_cost < dp[vecin][3]){
dp[vecin][3] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][3],make_pair(vecin,3)));
}
} else {
if (stare == 2){
if (dist_s[nod] + new_cost + dist_t[vecin] == dist_s[t]){ /// pot sa pastrez starea asta
if (dp[nod][stare] < dp[vecin][stare]){
dp[vecin][stare] = dp[nod][stare];
c.push(make_pair(dp[vecin][stare],make_pair(vecin,stare)));
}
}
/// trec in starea 3
if (dp[nod][stare] + new_cost < dp[vecin][3]){
dp[vecin][3] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][3],make_pair(vecin,3)));
}
} else { /// stare == 3
/// acum pot doar sa trec in starea 3
if (dp[nod][stare] + new_cost < dp[vecin][stare]){
dp[vecin][stare] = dp[nod][stare] + new_cost;
c.push(make_pair(dp[vecin][stare],make_pair(vecin,stare)));
}}}}}}
cout<<min(min(dp[v][0],dp[v][1]),min(dp[v][2],dp[v][3]));
return 0;
}
