#include <bits/stdc++.h>
#define ll long long
#define ldb long double
#define endl '\n'
#define For(i,l,r) for(int i=l;i<=r;i++)
#define ForD(i,r,l) for(int i=r;i>=l;i--)
#define REP(i,l,r) For(i,l,r-1)
#define PER(i,r,l) ForD(i,r-1,l)
#define ff first
#define ss second
#define pb emplace_back
#define all(x) x.begin(),x.end()
#define All(x,n) x+1,x+1+n
#define Alll(x,n) x,x+n
#define sz(x) (signed)x.size()
#define unq(x) x.resize(unique(all(x))-x.begin())
#define mpa make_pair
#ifdef NCGM
#include"debug.h"
#else
#define debug(...) "fr";
#endif
using namespace std;
const int N=4e5+9;
const ll INF=1e17;
struct edge {
int u,v,w;
edge(int k=0,int x=0,int y=0): u(k),v(x),w(y) {};
};
int n,m,a,b,c,d;
vector<edge> g[N],g1[N],g2[N];
vector<int> topo;
edge ed[N];
ll dis[N],dis1[N],f[N];
bool vs[N];
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
void dijkstra(int u,ll *out) {
fill(out,out+n+1,INF);
out[u]=0;
pq.push(mpa(0,u));
while(sz(pq)) {
ll w=pq.top().ff;
int cu=pq.top().ss;
pq.pop();
for(auto v: g[cu]) {
if (out[v.v]>v.w+w) {
out[v.v]=v.w+w;
pq.push(mpa(out[v.v],v.v));
}
}
}
}
void dfs(int u) {
vs[u]=1;
for(auto v: g1[u]) if (!vs[v.v]) dfs(v.v);
topo.pb(u);
}
ll solve() {
ll ans=1e17;
fill(f,f+n+2,INF);
for(auto u: topo) {
f[u]=dis[u];
for(auto v: g2[u]) f[u]=min(f[u],f[v.v]);
ans=min(ans,f[u]+dis1[u]);
}
return ans;
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> a >> b >> c >> d;
For(i,1,m) {
int u,v,w;
cin >> u >> v >> w;
ed[i]=edge(u,v,w);
g[u].pb(edge(u,v,w));
g[v].pb(edge(v,u,w));
}
dijkstra(a,dis);
dijkstra(b,dis1);
For(i,1,m) {
if (dis[ed[i].u]+dis1[ed[i].v]+ed[i].w==dis[b]) {
g1[ed[i].u].pb(ed[i]);
g2[ed[i].v].pb(edge(ed[i].v,ed[i].u,ed[i].w));
}
if (dis[ed[i].v]+dis1[ed[i].u]+ed[i].w==dis[b]) {
g1[ed[i].v].pb(edge(ed[i].v,ed[i].u,ed[i].w));
g2[ed[i].u].pb(ed[i]);
}
}
dijkstra(c,dis);
dijkstra(d,dis1);
For(i,1,n) if (!vs[i]) dfs(i);
reverse(all(topo));
ll res=dis[d];
res=min(res,solve());
swap(dis,dis1);
res=min(res,solve());
cout << res;
return 0;
}
