#include<bits/stdc++.h>
#define int long long
using namespace std;
int N, M, S, T, U, V;
vector<long long> DistancesFromS, DistancesFromT, DistancesFromU, DistancesFromV, DPfromUDAG1, DPfromUDAG2, DPfromVDAG1, DPfromVDAG2;
vector<vector<int>> edges, DAG1, DAG2;
vector<vector<pair<int, int>>> AdjList;
void Dijkstra(int start, vector<long long>& distances){
priority_queue<pair<long long, int>> PQ;
PQ.push({-0, start});
while(!PQ.empty()){
pair<int, int> act = PQ.top(); PQ.pop();
int NodeAct = act.second;
long long DistAct = -1*act.first;
if(distances[NodeAct] != -1) continue;
distances[NodeAct] = DistAct;
for(pair<int, int> next : AdjList[NodeAct]){
int neighbour = next.first;
long long cost = (long long)next.second;
if(distances[neighbour] == -1)PQ.push({-((long long)DistAct+cost), neighbour});
}
}
}
void fillDPDAG1WithU(int node){
//cout << "nodo " << node << " DP from U in DAG1 " << DPfromUDAG1[node] << endl;
//cout << "nodo " << node << " DP from V in DAG1 " << DPfromVDAG1[node] << endl;
for(int son: DAG1[node]){
long long proposal = min(DPfromUDAG1[node], DistancesFromU[son]);
if(DPfromUDAG1[son] <= proposal) continue;
DPfromUDAG1[son] = proposal;
fillDPDAG1WithU(son);
}
}
void fillDPDAG1WithV(int node){
//cout << "nodo " << node << " DP from U in DAG1 " << DPfromUDAG1[node] << endl;
//cout << "nodo " << node << " DP from V in DAG1 " << DPfromVDAG1[node] << endl;
for(int son: DAG1[node]){
long long proposal = min(DPfromVDAG1[node], DistancesFromV[son]);
if(DPfromVDAG1[son] <= proposal) continue;
DPfromVDAG1[son] = proposal;
fillDPDAG1WithV(son);
}
}
void fillDPDAG2WithU(int node){
for(int son: DAG2[node]){
long long proposal = min(DPfromUDAG2[node], DistancesFromU[son]);
if(DPfromUDAG2[son] <= proposal) continue;
DPfromUDAG2[son] = proposal;
fillDPDAG2WithU(son);
}
}
void fillDPDAG2WithV(int node){
for(int son: DAG2[node]){
long long proposal = min(DPfromVDAG2[node], DistancesFromV[son]);
if(DPfromVDAG2[son] <= proposal) continue;
DPfromVDAG2[son] = proposal;
fillDPDAG2WithV(son);
}
}
signed main(){
cin >> N >> M >> S >> T >> U >> V;
S--; T--; U--; V--;
int a, b, c;
edges = vector<vector<int>> (M, vector<int>(3));
AdjList = vector<vector<pair<int, int>>> (N);
for(int i = 0; i < M; ++i){
cin >> a >> b >> c; a--; b--;
AdjList[a].push_back({b, c});
AdjList[b].push_back({a, c});
edges[i][0] = a;
edges[i][1] = b;
edges[i][2] = c;
}
DistancesFromS = vector<long long>(N, -1);
DistancesFromT = vector<long long>(N, -1);
DistancesFromU = vector<long long>(N, -1);
DistancesFromV = vector<long long>(N, -1);
//cout << "First i/o ok" << endl;
Dijkstra(S, DistancesFromS);
Dijkstra(T, DistancesFromT);
Dijkstra(U, DistancesFromU);
Dijkstra(V, DistancesFromV);
//cout << "Dijkstras ok" << endl;
DAG1 = vector<vector<int>> (N);//DAG1 de S a T
DAG2 = vector<vector<int>> (N);//DAG2 de T a S
int minCost = DistancesFromS[T];
vector<bool> AreInDAG(N, false);
for(vector<int> edge: edges){
//cout << edge[0] << " " << edge[1] << " " << edge[2] << endl;
if((DistancesFromS[edge[0]] + DistancesFromT[edge[1]] + edge[2]) == minCost){
//uso de a->b para ir de S a T
DAG1[edge[0]].push_back(edge[1]);
DAG2[edge[1]].push_back(edge[0]);
AreInDAG[edge[0]] = true;
AreInDAG[edge[1]] = true;
//cout << "edge in DAG1 from " << edge[0] << " to " << edge[1] << endl;
//cout << "edge in DAG2 from " << edge[1] << " to " << edge[0] << endl;
}
else if((DistancesFromT[edge[0]] + DistancesFromS[edge[1]] + edge[2]) == minCost){
//uso de b->a para ir de S a T
DAG1[edge[1]].push_back(edge[0]);
DAG2[edge[0]].push_back(edge[1]);
AreInDAG[edge[0]] = true;
AreInDAG[edge[1]] = true;
//cout << "edge in DAG1 from " << edge[1] << " to " << edge[0] << endl;
//cout << "edge in DAG2 from " << edge[0] << " to " << edge[1] << endl;
}
}
DPfromUDAG1 = vector<long long>(N, 1e17);
DPfromUDAG1[S] = DistancesFromU[S];
DPfromUDAG2 = vector<long long>(N, 1e17);
DPfromUDAG2[T] = DistancesFromU[T];
DPfromVDAG1 = vector<long long>(N, 1e17);
DPfromVDAG1[S] = DistancesFromV[S];
DPfromVDAG2 = vector<long long>(N, 1e17);
DPfromVDAG2[T] = DistancesFromV[T];
fillDPDAG1WithU(S);
fillDPDAG1WithV(S);
//cout << "First dp ok" << endl;
fillDPDAG2WithU(T);
fillDPDAG2WithV(T);
//cout << "Second dp ok" << endl;
/*
for(int i = 1; i <= N; ++i){
cout << "node " << i << " dist from U " << DistancesFromU[i-1] << " dist from V " << DistancesFromV[i-1] << endl;
}*/
long long ans = DistancesFromU[V];
//cout << ans << endl;
for(int node = 0; node < N; ++node){
if(AreInDAG[node]) {
ans = min(ans, min(DPfromVDAG2[node]+DPfromUDAG1[node], DPfromVDAG1[node]+DPfromUDAG2[node]));
//cout << ans << endl;
}
}
cout << ans << endl;
return 0;
}
