#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll INF=LONG_LONG_MAX;
ll m, n, s, t, u, v;
vector<pair<ll, ll> >graff[200010];
vector<ll>dag[200010];
bool check1[200010], check2[200010];
ll distu[200010], distv[200010], dists[200010], distt[200010];
ll res=INF;
set<pair<ll,ll> > grane;
void dijkstra(ll cvor, ll *dist)
{
for(int i=0; i<100010; i++)
{
check1[i]=false;
dist[i]=INF;
}
priority_queue<pair<ll, ll> >ord;
dist[cvor]=0;
ord.push({0, cvor});
while(!ord.empty())
{
int cv=ord.top().second;
ord.pop();
if(check1[cv])continue;
check1[cv]=true;
for(int j=0; j<graff[cv].size(); j++)
{
ll pp=graff[cv][j].first;
dist[pp]=min(dist[pp], dist[cv]+graff[cv][j].second);
if(!check1[pp])ord.push({-dist[pp], pp});
}
}
}
void dfs1(ll prosli, ll cvor)
{
if(dists[cvor]+distt[cvor]!=dists[t])return;
if(dists[cvor]-dists[prosli]<0)return;
dag[prosli].push_back(cvor);
if(cvor==t)return;
for(int i=0; i<graff[cvor].size(); i++)
{
if (dists[cvor]+graff[cvor][i].second+distt[graff[cvor][i].first]==dists[t] && !grane.count({cvor, graff[cvor][i].first}))
{
grane.insert({cvor, graff[cvor][i].first});
dfs1(cvor, graff[cvor][i].first);
}
}
return;
}
void solve()///zamena za dfs2
{
priority_queue<pair<ll,ll> > q;
ll U[100010],V[100010];
for (ll i=1;i<=n;i++)
{
U[i]=INF;
V[i]=INF;
}
U[s]=distu[s];
V[s]=distv[s];
q.push({-U[s],s});
while (!q.empty())
{
ll t=q.top().second,d=abs(q.top().first);
q.pop();
if (U[t]!=d)
continue;
res=min(res,U[t]+V[t]);
for (auto next : dag[t])
{
ll i=next;
if (U[i]==INF)
{
U[i]=distu[i];
V[i]=distv[i];
q.push({-U[i],i});
}
if (U[t]<U[i])
{
U[i]=U[t];
V[i]=min(distv[i],V[t]);
q.push({-U[i],i});
}
else if (U[t]==U[i])
{
if (V[i]<=V[t])
V[i]=distv[i];
else
{
V[i]=V[t];
q.push({-U[i],i});
}
}
}
}
for (ll i=1;i<=n;i++)
{
U[i]=INF;
V[i]=INF;
}
U[s]=distu[s];
V[s]=distv[s];
q.push({-V[s],s});
while (!q.empty())
{
ll t=q.top().second,d=abs(q.top().first);
q.pop();
if (V[t]!=d)
continue;
res=min(res,U[t]+V[t]);
for (auto next : dag[t])
{
ll i=next;
if (V[i]==INF)
{
V[i]=distv[i];
U[i]=distu[i];
q.push({-V[i],i});
}
if (V[t]<V[i])
{
V[i]=V[t];
U[i]=min(distu[i],U[t]);
q.push({-V[i],i});
}
else if (V[t]==V[i])
{
if (U[i]<=U[t])
U[i]=distu[i];
else
{
U[i]=U[t];
q.push({-V[i],i});
}
}
}
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie();
cout.tie();
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
ll a, b, c;
for(int i=0; i<m; i++)
{
cin>>a>>b>>c;
graff[a].push_back({b, c});
graff[b].push_back({a, c});
}
dijkstra(u, distu);
dijkstra(v, distv);
dijkstra(s, dists);
dijkstra(t, distt);
dists[0]=0;
dfs1(0, s);
solve();
cout<<min(res, distv[u]);
return 0;
}
