#include<bits/stdc++.h>
#define int long long
using namespace std;
vector<pair<int, int>> ad[400005];
vector<int> optimal[400005];
int dis[400005];
bool visited[400005];
void dijkstra(int s)
{
memset(dis, 0x3f, sizeof(dis));
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> w;
dis[s] = 0; w.push({0, s});
while(w.size() > 0){
int u = w.top().second, d = w.top().first;
w.pop();
if(dis[u] != d) continue;
for(pair<int, int> i : ad[u]){
int v = i.first, c = i.second;
if(dis[v] > d+c){
optimal[v].clear();
w.push({d+c, v});
}
if(dis[v] >= d+c){
dis[v] = d+c;
optimal[v].push_back(u);
}
}
}
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m, s, t, ss, tt; cin>>n>>m>>s>>t>>ss>>tt;
vector<pair<pair<int, int>, int>> edges;
for(int i = 1; i <= m; i++){
int u, v, c; cin>>u>>v>>c;
ad[u].push_back({v, c});
ad[v].push_back({u, c});
edges.push_back({{u, v}, c});
edges.push_back({{v, u}, c});
}
dijkstra(s);
//Some traceback
queue<int> w; w.push(t); visited[t] = 1;
while(w.size() > 0){
int u = w.front(); w.pop();
for(int v : optimal[u]) if(visited[v] == 0){
w.push(v);
visited[v] = 1;
}
}
for(int i = 1; i <= n; i++) if(visited[i] == 0) dis[i] = -1e18;
for(int i = 1; i <= n; i++){ad[i].clear(); optimal[i].clear();}
for(auto i : edges){
int u = i.first.first, v = i.first.second, c = i.second;
if(dis[v] == dis[u] + c){
//cerr<<"A"<<u<<" "<<v<<endl;
ad[u].push_back({v+n, 0});
ad[u+n].push_back({v+n, 0});
}
else if(dis[u] == dis[v]+c){
ad[u].push_back({v+2*n, 0});
ad[u+2*n].push_back({v+2*n, 0});
}
ad[u].push_back({v, c});
ad[u+n].push_back({v+3*n, c});
ad[u+2*n].push_back({v+3*n, c});
ad[u+3*n].push_back({v+3*n, c});
}
dijkstra(ss);
cout<<min({dis[tt], dis[tt+n], dis[tt+n+n], dis[tt+n+n+n]});
}
