#include "bits/stdc++.h"
using namespace std;
#define int long long
#define fi first
#define se second
#define pii pair<int,int>
#define pll pair<long long,long long>
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define pb push_back
#define ll long long
#define mp make_pair
const ll inf = 1e17;
const int N = 2e5+5;
int n,m;
int A,B,C,D;
vector<pii> g[N];
void predij(int st, ll d[]){
for(int i=1;i<=n;i++) d[i]= inf;
priority_queue<pll, vector<pll>, greater<pll>>pq;
pq.push({d[st]=0, st});
while(!pq.empty()){
ll du = pq.top().fi, u= pq.top().se;
pq.pop();
if(du!=d[u]) continue;
for(auto &x: g[u]){
int v= x.fi, uv= x.se;
if(d[v]> d[u]+uv) {
pq.push({d[v]= du+uv, v});
}
}
}
}
ll dc[N], dd[N];
pll d[N][5];
struct Node{
ll du, u, t, c;
bool operator <(const Node &o)const{
if(du==o.du){
return c> o.c;
}
return du > o.du;
}
};
void dij(){
priority_queue<Node> pq;
d[A][0] = {0,0};
d[A][1] = {0,dc[A]};
d[A][2] = {0,dc[A]+ dd[A]};
pq.push({0,A,0,0});
pq.push({0,A,1,dc[A]});
pq.push({0,A,2,dc[A]+dd[A]});
while(!pq.empty()){
Node top = pq.top();
pq.pop();
ll du = top.du, u= top.u, t= top.t, c= top.c;
if(mp(du,c)!=d[u][t]) continue;
for(auto &x: g[u]){
int v= x.fi, uv = x.se;
if(t==0){
if(d[v][0]> mp(du+uv, c)){
d[v][0] = mp(du+uv,c);
pq.push({du+uv, v, 0, c});
}
if(d[v][1]> mp(du+uv, c+ dc[v])){
d[v][1] = mp(du+uv, c+dc[v]);
pq.push({du+uv, v, 1, c+ dc[v]});
}
if(d[v][2]>mp(du+uv, c+dc[v]+dd[v])){
d[v][2] = mp(du+uv, c+dc[v]+dd[v]);
pq.push({du+uv, v, 2, c+ dc[v]+dd[v]});
}
}
else if(t==1){
if(d[v][1]> mp(du+uv, c)){
d[v][1] = mp(du+uv,c);
pq.push({du+uv, v, 1, c});
}
if(d[v][2]> mp(du+uv, c+ dd[v])){
d[v][2] = mp(du+uv, c+dd[v]);
pq.push({du+uv, v, 2, c+ dd[v]});
}
}
else{
if(d[v][2]> mp(du+uv, c)){
d[v][2] = mp(du+uv,c);
pq.push({du+uv, v, 2, c});
}
}
}
}
}
signed main(){
ios_base::sync_with_stdio(NULL);
cin.tie(NULL);
if(fopen("tunnel.INP", "r")){
freopen("tunnel.INP", "r", stdin);
freopen("tunnel.OUT", "w", stdout);
}
cin>>n>>m;
cin>>A>>B>>C>>D;
for(int i=1;i<=m;i++){
int u,v,w; cin>>u>>v>>w;
g[u].pb({v,w});
g[v].pb({u,w});
}
fill_n(&d[0][0], sizeof(d)/sizeof(d[0][0]), mp(inf,inf));
predij(C,dc);
predij(D,dd);
dij();
ll res1 =d[B][2].se;
fill_n(&d[0][0], sizeof(d)/sizeof(d[0][0]), mp(inf,inf));
predij(D,dc);
predij(C,dd);
dij();
ll res2 = d[B][2].se;
cout<<min({res1,res2, dc[C]});
}
