#include <iostream>
#include <set>
#include <vector>
using namespace std;
#define int long long
const int N = 2e5 + 10;
int dist[5][N], seen[N], a[N], b[N], c[N], U[N], V[N];
vector<pair<int,int>> nei[N];
vector<int> dag[N], vec;
void dfs(int u){
seen[u] = 1;
for (int i : dag[u]){
if (seen[i] == 0)
dfs(i);
}
// cout<<u<<endl;
vec.push_back(u);
}
void dijkstra(int s, int id){
for (int i=1;i<N;i++)
dist[id][i] = U[i] = V[i] = 1e17;
dist[id][s] = 0;
set<pair<int,int>> st = {{0, s}};
while (st.size() > 0){
auto [dt, u] = *begin(st);
st.erase(begin(st));
for (auto [i, w] : nei[u]){
if (dist[id][i] > dist[id][u] + w){
st.erase({dist[id][i], i});
dist[id][i] = dist[id][u] + w;
st.insert({dist[id][i], i});
}
}
}
}
signed main(){
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
int n, m, s, t, u, v;
cin>>n>>m>>s>>t>>u>>v;
for (int i=1;i<=m;i++){
cin>>a[i]>>b[i]>>c[i];
nei[a[i]].push_back({b[i], c[i]});
nei[b[i]].push_back({a[i], c[i]});
}
dijkstra(u, 1);
dijkstra(v, 2);
dijkstra(s, 3);
dijkstra(t, 4);
for (int i=1;i<=m;i++){
for (int j : {0, 1}){
swap(a[i], b[i]);
if (dist[3][a[i]] + dist[4][b[i]] + c[i] == dist[3][t])
dag[a[i]].push_back(b[i]);
}
}
for (int i=1;i<=n;i++){
if (!seen[i])
dfs(i);
}
int Ans = dist[1][v];
for (int i : vec){
U[i] = dist[1][i];
V[i] = dist[2][i];
for (int j : dag[i]){
U[i] = min(U[i], U[j]);
V[i] = min(V[i], V[j]);
}
Ans = min(Ans, min(dist[1][i] + V[i], dist[2][i] + U[i]));
}
cout<<Ans<<'\n';
}
