#include<bits/stdc++.h>
using namespace std;
#define range(v) begin(v), end(v)
#define compact(v) v.erase(unique(range(v)), end(v))
#define len(x) (int)(x).size()
#define BIT(x, i) ((x)>>(i)&1)
#define MASK(x) (1LL<<(x))
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
template<class T> bool maximize(T& a, const T& b){ if(a<b) return a=b, true; return false; }
template<class T> bool minimize(T& a, const T& b){ if(a>b) return a=b, true; return false; }
const int N=1e5+5;
struct edge{
int u, v, w;
} e[N*2];
struct item{
int v, w, id;
};
int n, m, s, t, U, V;
vector<item> g[N];
bool in_shortest_path[N*2];
vector<ll> dijkstra(int st){
vector<ll> d(n+1, -1); d[st]=0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({0, st});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(d[u]!=cost) continue;
for(int i=0; i<g[u].size(); ++i){
int v=g[u][i].v, w=g[u][i].w;
if(d[v]==-1 or (d[v]>(d[u]+w))){
d[v]=d[u]+w;
pq.push({d[v], v});
}
}
}
return d;
}
ll modify_dijkstra(int st, int ed){
vector<ll> d(n+1, -1); d[st]=0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({0, st});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(cost!=d[u]) continue;
for(int i=0; i<g[u].size(); ++i){
int v=g[u][i].v, w=(in_shortest_path[g[u][i].id]?0:g[u][i].w);
if(d[v]==-1 or (d[v]>(d[u]+w))){
d[v]=d[u]+w;
pq.push({d[v], v});
}
}
}
return d[ed];
}
void Zero_OP(){
cin>>n>>m>>s>>t>>U>>V;
for(int i=1; i<=m; ++i){
int u, v, c; cin>>u>>v>>c;
g[u].push_back({v, c, i});
g[v].push_back({u, c, i});
e[i]={u, v, c};
}
if(n<=300){
ll d[n+1][n+1];
memset(d, 0x3f, sizeof(d));
for(int i=1; i<=m; ++i){
minimize(d[e[i].u][e[i].v], (ll)e[i].w);
minimize(d[e[i].v][e[i].u], (ll)e[i].w);
}
for(int k=1; k<=n; ++k){
for(int i=1; i<=n; ++i){
for(int j=1; j<=n; ++j){
minimize(d[i][j], d[i][k]+d[k][j]);
}
}
}
ll ans=d[U][V];
for(int i=1; i<=n; ++i){
for(int j=1; j<=n; ++j){
if(d[s][i]+d[i][j]+d[j][t]==d[s][t]){
minimize(ans, min(d[U][i]+d[j][V], d[V][i]+d[j][U]));
}
}
}
cout<<ans;
}
else {
vector<ll> d_s=dijkstra(s), d_t=dijkstra(t);
for(int i=1; i<=m; ++i){
int u=e[i].u, v=e[i].v, w=e[i].w;
if(d_s[u]+w+d_t[v]==d_s[t] or d_s[v]+w+d_t[u]==d_s[t]){
in_shortest_path[i]=true;
}
}
cout<<modify_dijkstra(U, V);
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL); cout.tie(NULL);
#define task "COMPUTER_PASS"
if(fopen(task".INP", "r")){
freopen(task".INP", "r", stdin);
freopen(task".OUT", "w", stdout);
}
int TC=1; //cin>>TC;
while(TC--) Zero_OP();
return 0;
}
