#include<bits/stdc++.h>
#define TASKNAME "codeforce"
#define pb push_back
#define pli pair<ll,ll>
#define fi first
#define se second
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL);
using namespace std;
using ll=long long;
const ll maxN=3e5;
const ll inf=1e18;
const ll mod=1e9+7;
ll n,d[3][maxN];
bool vis[maxN];
vector<pli>g[maxN],adj[maxN],ke[maxN];
void dij(ll s,ll t)
{
for(int i=1;i<=n;i++) d[t][i]=inf,vis[i]=false;
d[t][s]=0;
priority_queue<pli,vector<pli>,greater<pli>>pq;
pq.push({d[t][s],s});
while(!pq.empty())
{
ll u=pq.top().se;
pq.pop();
if(vis[u]==true) continue;
vis[u]=true;
for(auto vv:g[u])
{
ll v=vv.fi;
ll w=vv.se;
if(d[t][v]>d[t][u]+w)
{
d[t][v]=d[t][u]+w;
pq.push({d[t][v],v});
}
}
}
}
ll m,s,t,x,y;
struct qq
{
ll u,v,w;
}a[maxN];
void solve()
{
cin >> n >> m;
cin >> s >> t;
cin >> x >> y;
for(int i=1;i<=m;i++)
{
ll u,v,w;
cin >> u >> v >> w;
a[i].u=u;
a[i].v=v;
a[i].w=w;
g[u].pb({v,w});
g[v].pb({u,w});
}
dij(s,0);
dij(t,1);
for(int i=1;i<=m;i++)
{
if(d[0][a[i].u]+d[1][a[i].v]+a[i].w==d[0][t])
{
adj[a[i].u].pb({a[i].v,0});
adj[a[i].v].pb({a[i].u,a[i].w});
}
else if(d[0][a[i].v]+d[1][a[i].u]+a[i].w==d[0][t])
{
adj[a[i].v].pb({a[i].u,0});
adj[a[i].u].pb({a[i].v,a[i].w});
}
else
{
adj[a[i].u].pb({a[i].v,a[i].w});
adj[a[i].v].pb({a[i].u,a[i].w});
}
}
for(int i=1;i<=n;i++) swap(adj[i],g[i]);
ll ans=inf;
dij(x,0);
ans=d[0][y];
for(int i=1;i<=n;i++) swap(ke[i],g[i]);
dij(x,0);
ans=min(ans,d[0][y]);
cout << ans <<'\n';
}
int main()
{
fastio
//freopen(TASKNAME".INP","r",stdin);
//freopen(TASKNAME".OUT","w",stdout);
solve();
}
