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