#include <bits/stdc++.h>
using namespace std;
const long long inf = 1e18;
vector<long long> dijkstra(int source, const vector<vector<pair<int, long long> > > &graph){
vector<long long> dist(graph.size(), inf);
dist[source] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > pq;
pq.push({dist[source], source});
while(!pq.empty()){
int nod = pq.top().second;
long long cost = pq.top().first;
pq.pop();
if(cost != dist[nod]){
continue;
}
for(auto it:graph[nod]){
if(dist[it.first] > dist[nod] + it.second){
dist[it.first] = dist[nod] + it.second;
pq.push({dist[it.first], it.first});
}
}
}
return dist;
}
long long best_distance(const vector<long long> &dist_u, const vector<long long> &dist_v, vector<vector<pair<int, long long> > > &graph, const vector<pair<int,int> > &edges, int n){
for(auto it:dist_u)printf("%lld ", it);printf("\n");
for(auto it:dist_v)printf("%lld ", it);printf("\n");
for(int i = 0;i < n;i++){
graph[i].clear();
}
for(auto it:edges){
graph[it.first].push_back({it.second, dist_v[it.second] - dist_v[it.first]});
// printf("edge from %d to %d with cost %lld\n", it.first, it.second, dist_v[it.second] - dist_v[it.first]);
}
if((int)graph.size() < n + 1){
graph.push_back(vector<pair<int, long long> >());
}else{
graph[n].clear();
}
for(int i = 0;i < n;i++){
graph[n].push_back({i, dist_u[i] + dist_v[i]});
// printf("edge from %d to %d with cost %lld\n", n, i, dist_u[i] + dist_v[i]);
}
//printf("\n");
vector<long long> dist = dijkstra(n, graph);
long long best_dist = inf;
for(int i = 0;i < n;i++){
best_dist = min(best_dist, dist[i]);
}
return best_dist;
}
int main(){
int n, m;
int s, t;
int u, v;
scanf("%d %d", &n, &m);
scanf("%d %d", &s, &t);
scanf("%d %d", &u, &v);
s--;
v--;
t--;
u--;
vector<vector<pair<int, long long> > > graph(n, vector<pair<int, long long> >());
vector<pair<pair<int, int>,int> > edges;
for(int i = 1;i <= m;i++){
int a, b, c;
scanf("%d %d %d", &a, &b, &c);
a--;
b--;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
edges.push_back({{a, b}, c});
}
vector<long long> dist_s = dijkstra(s, graph);
vector<long long> dist_t = dijkstra(t, graph);
vector<long long> dist_u = dijkstra(u, graph);
vector<long long> dist_v = dijkstra(v, graph);
vector<pair<int, int> > new_edges;
for(auto it:edges){
if(dist_t[it.first.first] + dist_s[it.first.second] + it.second == dist_s[t]){
new_edges.push_back({it.first.second, it.first.first});
}
if(dist_s[it.first.first] + dist_t[it.first.second] + it.second == dist_s[t]){
new_edges.push_back({it.first.first, it.first.second});
}
}
long long fst = best_distance(dist_u, dist_v, graph, new_edges, n);
long long snd = best_distance(dist_v, dist_u, graph, new_edges, n);
long long trd = dist_u[v];
printf("%lld\n", min(min(fst, snd), trd));
return 0;
}
