#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define X first
#define Y second
#define ll long long
ll n,m,S,T,U,V,a,b,c,disu[100005],disv[100005],dp[100005],ans=1e18,d[100005],u,node,cost,y;
ll dp2[100005],d2[100005];
vector<pair<ll,ll> > v[100005];
priority_queue<pair<ll,ll> > pq;
void dij(ll st,ll dis[])
{
for(int i=1;i<=n;i++)dis[i]=1e18;
dis[st]=0;
pq.push({0,st});
while(!pq.empty())
{
u=pq.top().Y;
pq.pop();
for(int i=0;i<v[u].size();i++)
{
node=v[u][i].X,cost=v[u][i].Y;
if(dis[u]+cost<dis[node])
{
dis[node]=dis[u]+cost;
pq.push({-dis[node],node});
}
}
}
}
int main()
{
scanf("%lld%lld%lld%lld%lld%lld",&n,&m,&S,&T,&U,&V);
for(int i=1;i<=m;i++)
{
scanf("%lld%lld%lld",&a,&b,&c);
v[a].pb({b,c});
v[b].pb({a,c});
}
dij(U,disu),dij(V,disv);
for(int i=1;i<=n;i++)dp[i]=1e18,d[i]=1e18,d2[i]=1e18,dp2[i]=1e18;
dp[S]=disu[S],d[S]=0;
ans=min(ans,disu[S]+disv[S]);
pq.push({-d[S],S});
while(!pq.empty())
{
u=pq.top().Y;
pq.pop();
for(int i=0;i<v[u].size();i++)
{
y=v[u][i].X,cost=v[u][i].Y;
if(d[u]+cost<=d[y])
{
d[y]=d[u]+cost;
dp[y]=min(dp[y],min(dp[u],disu[y]));
pq.push({-d[y],y});
}
}
}
dp2[T]=disu[T],d2[T]=0;
ans=min(ans,disu[T]+disv[T]);
pq.push({-d2[T],T});
while(!pq.empty())
{
u=pq.top().Y;
pq.pop();
for(int i=0;i<v[u].size();i++)
{
y=v[u][i].X,cost=v[u][i].Y;
if(d2[u]+cost<=d2[y])
{
d2[y]=d2[u]+cost;
dp2[y]=min(dp2[y],min(dp2[u],disu[y]));
pq.push({-d2[y],y});
}
}
}
/*for(int i=1;i<=n;i++)
{
printf("%lld %lld %lld %lld\n",d[i],d2[i],dp[i],dp2[i]);
}*/
for(int i=1;i<=n;i++)
{
if(d[i]+d2[i]==d[T])
{
ans=min(ans,min(dp[i],dp2[i])+disv[i]);
}
}
printf("%lld\n",ans);
}
