#include <bits/stdc++.h>
#define pii pair<int,int>
#define pli pair<long long,int>
#define iii pair<int,pii>
#define fi first
#define se second
#define vi vector<int>
#define vii vector<pii>
#define pb(i) push_back(i)
#define all(x) x.begin(),x.end()
#define TEXT "a"
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const ll inf = 1e15 + 5;
const ld eps = 1e-8;
const double pi = acos(-1);
const int N = 1e5 + 5;
vector<pii> a[N];
vector<int> b[N], c[N];
vector<ll> dS, dT, dX, dY;
ll f[N], g[N];
int n,m;
int s,t,x,y;
void dijkstra(int s, vector<ll>& d){
d.resize(n + 5,inf);
priority_queue<pli,vector<pli>,greater<pli>> pq;
d[s] = 0;
pq.push(pli(0,s));
while(!pq.empty()){
int u = pq.top().se;
ll dis = pq.top().fi;
pq.pop();
if (dis > d[u]) continue;
for (int i = 0; i < a[u].size(); i++){
int v = a[u][i].fi;
int w = a[u][i].se;
if (d[u] + w < d[v]){
d[v] = d[u] + w;
pq.push(pli(d[v],v));
}
}
}
}
void buildGraph(){
for (int u = 1; u <= n; u++){
for (int i = 0; i < a[u].size(); i++){
int v = a[u][i].fi;
int w = a[u][i].se;
if (dS[v] == dS[u] + w && dS[t] == dS[u] + w + dT[v]){
b[u].push_back(v);
c[v].push_back(u);
//cout << u << " " << v << " " << w << "\n";
}
}
}
}
void calX(int u){
if (f[u] != inf) return;
f[u] = dX[u];
for (int v : c[u]){
calX(v);
f[u] = min(f[u], f[v]);
}
}
void calY(int u){
if (g[u] != inf) return;
g[u] = dY[u];
for (int v : b[u]){
calY(v);
g[u] = min(g[u], g[v]);
}
}
int main(){
cin.tie(0) -> sync_with_stdio(0);
if (fopen(TEXT".inp","r")){
freopen(TEXT".inp","r",stdin);
freopen(TEXT".out","w",stdout);
}
cin >> n >> m;
cin >> s >> t >> x >> y;
for (int i = 1; i <= m; i++){
int u,v,w;
cin >> u >> v >> w;
a[u].pb(pii(v,w));
a[v].pb(pii(u,w));
}
dijkstra(s, dS);
dijkstra(t, dT);
//cout << "-----\n";
buildGraph();
//cout << "-----\n";
dijkstra(x, dX);
dijkstra(y, dY);
for (int i = 1; i <= n; i++) f[i] = g[i] = inf;
calX(t);
calY(s);
ll res = dX[y];
for (int i = 1; i <= n; i++){
res = min(res,f[i] + g[i]);
}
for (int i = 1; i <= n; i++) f[i] = g[i] = inf;
swap(x, y);
swap(dX, dY);
calX(t);
calY(s);
for (int i = 1; i <= n; i++){
res = min(res,f[i] + g[i]);
}
cout << res << "\n";
return 0;
}
