// Source: https://usaco.guide/general/io
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll cap = 2e5+1;
const ll INF = (ll)1e18;
vector<pair<ll,ll>> adj[cap];
vector<ll> dag[cap], rdag[cap];
ll indegree[cap];
ll distS[cap], distU[cap], distV[cap];
vector<tuple<ll,ll,ll>> edges;
priority_queue<pair<ll,ll>> pqs, pqu, pqv;
ll n, m;
ll s, t, u, v;
void dijkstra(){
pqs.push({0,s});
while(!pqs.empty()){
auto [nd,x] = pqs.top(); pqs.pop();
ll d = -nd;
if(d != distS[x]) continue;
for(auto [y,w]: adj[x]){
if(distS[x] + w < distS[y]){
distS[y] = distS[x] + w;
pqs.push({-distS[y], y});
}
}
}
pqu.push({0,u});
while(!pqu.empty()){
auto [nd,x] = pqu.top(); pqu.pop();
ll d = -nd;
if(d != distU[x]) continue;
for(auto [y,w]: adj[x]){
if(distU[x] + w < distU[y]){
distU[y] = distU[x] + w;
pqu.push({-distU[y], y});
}
}
}
pqv.push({0,v});
while(!pqv.empty()){
auto [nd,x] = pqv.top(); pqv.pop();
ll d = -nd;
if(d != distV[x]) continue;
for(auto [y,w]: adj[x]){
if(distV[x] + w < distV[y]){
distV[y] = distV[x] + w;
pqv.push({-distV[y], y});
}
}
}
}
ll solve(){
for(ll i=1;i<=n;i++){
dag[i].clear();
rdag[i].clear();
indegree[i]=0;
}
fill(distS,distS+cap,INF);
fill(distU,distU+cap,INF);
fill(distV,distV+cap,INF);
while(!pqs.empty()) pqs.pop();
while(!pqu.empty()) pqu.pop();
while(!pqv.empty()) pqv.pop();
distS[s]=0;
distU[u]=0;
distV[v]=0;
dijkstra();
for(auto [a,b,w]: edges){
if(distS[a]+w==distS[b]){
dag[a].push_back(b);
rdag[b].push_back(a);
}
if(distS[b]+w==distS[a]){
dag[b].push_back(a);
rdag[a].push_back(b);
}
}
vector<char> good(n+1,0);
queue<ll> qq;
good[t]=1;
qq.push(t);
while(!qq.empty()){
ll x=qq.front(); qq.pop();
for(ll y: rdag[x]){
if(!good[y]){
good[y]=1;
qq.push(y);
}
}
}
for(ll i=1;i<=n;i++){
if(!good[i]) continue;
for(ll j: dag[i]){
if(good[j]) indegree[j]++;
}
}
queue<ll> q;
vector<ll> topo;
for(ll i=1;i<=n;i++){
if(good[i] && indegree[i]==0) q.push(i);
}
while(!q.empty()){
ll x=q.front(); q.pop();
topo.push_back(x);
for(ll y: dag[x]){
if(!good[y]) continue;
if(--indegree[y]==0) q.push(y);
}
}
vector<ll> dp_entry(n+1,INF), dp_ans(n+1,INF);
for(ll x: topo){
dp_entry[x]=min(dp_entry[x],distU[x]);
dp_ans[x]=min(dp_ans[x],dp_entry[x]+distV[x]);
for(ll y: dag[x]){
if(!good[y]) continue;
dp_entry[y]=min(dp_entry[y],dp_entry[x]);
dp_ans[y]=min(dp_ans[y],dp_ans[x]);
}
}
ll best = min(distU[v], dp_ans[t]);
for (ll i = 1; i <= n; i++) {
if (good[i]) best = min(best, distU[i] + distV[i]);
}
for (ll a = 1; a <= n; a++) {
if (!good[a]) continue;
for (ll b : dag[a]) {
if (!good[b]) continue;
best = min(best, distU[a] + distV[b]);
best = min(best, distU[b] + distV[a]);
}
}
return best;
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin>>n>>m;
cin>>s>>t>>u>>v;
for(ll i=0;i<m;i++){
ll a,b,w; cin>>a>>b>>w;
adj[a].push_back({b,w});
adj[b].push_back({a,w});
edges.push_back({a,b,w});
}
ll ans1 = solve();
swap(s,t);
swap(u,v);
ll ans2 = solve();
cout << min(ans1, ans2);
}
