#include <iostream>
#include <vector>
#include <queue>
#include <utility>
using namespace std;
struct State{
long long v, dist;
vector<long long> path;
};
bool comp(const State &s1, const State &s2){
return s1.dist>s2.dist;
}
vector<vector<pair<long long, long long>>> graph;
vector<bool> found;
vector<pair<long long, long long>> freeEdges;
State Dijkstra(long long v1, long long v2, bool pathRecovery){
for (long long i=0;i<found.size();i++) found[i]=false;
priority_queue<State, vector<State>, bool (*)(const State &, const State &)> pq(comp);
pq.push(State{v1, 0, vector<long long>{v1}});
while (!pq.empty()){
State sta=pq.top();
pq.pop();
found[sta.v]=true;
if (sta.v==v2) return sta;
for (long long i=0;i<graph[sta.v].size();i++){
if (!found[graph[sta.v][i].first]){
long long addedCost=graph[sta.v][i].second;
if (graph[sta.v][i].first==freeEdges[sta.v].first||graph[sta.v][i].first==freeEdges[sta.v].second) addedCost=0;
if (pathRecovery){
vector<long long> temp=sta.path;
temp.push_back(graph[sta.v][i].first);
pq.push(State{graph[sta.v][i].first, sta.dist+addedCost, temp});
}
else pq.push(State{graph[sta.v][i].first, sta.dist+addedCost, sta.path});
}
}
}
return State{-1, -1, vector<long long>{}};
}
void PathOut(State sta){
freeEdges[sta.path[0]].second=sta.path[1];
freeEdges[sta.path[sta.path.size()-1]].first=sta.path[sta.path.size()-2];
for (long long i=1;i<sta.path.size()-1;i++){
freeEdges[sta.path[i]].first=sta.path[i-1];
freeEdges[sta.path[i]].second=sta.path[i+1];
}
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
long long n, m, s, t, u, v;
cin>>n>>m>>s>>t>>u>>v;
graph.resize(n+7);
found.resize(n+7);
freeEdges.resize(n+7);
for (long long i=0;i<m;i++){
long long v1, v2, c;
cin>>v1>>v2>>c;
graph[v1].push_back({v2, c});
graph[v2].push_back({v1, c});
}
PathOut(Dijkstra(s, t, true));
long long dist=Dijkstra(u, v, false).dist;
cout<<dist<<'\n';
return 0;
}
