#include <bits/stdc++.h>
using namespace std;
#define name "commuter"
#define MAXN 200005
#define pb push_back
#define pf push_front
#define ll long long
#define ii pair<int, int>
#define fs first
#define sc second
#define ill pair<int, ll>
#define lli pair<ll, int>
#define llll pair<ll, ll>
#define all(v) v.begin(),v.end()
#define uni(v) v.erase(unique(all(v)),v.end())
#define bit(n,i) (((n)>>(i))&1)
#define FOR(i,a,b) for (int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for (int i=(a),_b=(b); i>=_b; i--)
#define MASK(i) (1LL<<(i))
const ll INF=1e18;
const int MOD=1e9+7;
void add(int &u, int v){
u+=v;
if (u>=MOD) u-=MOD;
}
void sub(int &u, int v){
u-=v;
if (u<0) u+=MOD;
}
void minimize(ll &u, ll v){
u=min(u,v);
}
void maximize(int &u, int v){
u=max(u,v);
}
long long Rand(long long l, long long r){
ll tmp=0;
FOR(i,1,4) tmp=((tmp<<15)^(((1<<15)-1)&rand()));
return l+tmp%(r-l+1);
}
int n,m;
vector<ii> adj[MAXN];
vector<int> child[MAXN],par[MAXN];
int S,T,U,V;
ll d[3][MAXN];
bool visited[MAXN];
priority_queue<lli,vector<lli>,greater<lli>> pq;
void dijkstra(int type, int s){
FOR(i,1,n) d[type][i]=INF;
d[type][s]=0;
pq.push({0,s});
while (pq.size()){
lli tmp=pq.top();
pq.pop();
int u=tmp.sc;
if (visited[u]) continue;
visited[u]=1;
for (ii pairs:adj[u]){
int v=pairs.fs;
int wei=pairs.sc;
if (d[type][v]>d[type][u]+1LL*wei){
d[type][v]=d[type][u]+1LL*wei;
pq.push({d[type][v],v});
}
}
}
}
ll ans;
ll f[MAXN],g[MAXN];
void dfs(int type, int u){
if (type==1){
for (int v:child[u]){
f[v]=min(f[u],d[1][v]);
dfs(type,v);
}
}
else{
for (int v:par[u]){
g[v]=min(g[u],d[2][v]);
dfs(type,v);
}
}
}
struct edge{
int u,v,w;
}e[MAXN];
int Par[MAXN],lab[MAXN];
int main()
{
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
/*
srand(time(0));
n=Rand(1000,1000);
S=Rand(1,n);
T=Rand(1,n);
U=Rand(1,n);
V=Rand(1,n);
FOR(i,2,n) Par[i]=Rand(max(1LL,i-5),i-1);
FOR(i,1,n) lab[i]=i;
random_shuffle(lab+1,lab+n+1);
vector<ii> edges;
FOR(i,2,n){
int x=lab[i],y=lab[Par[i]];
if (rand()%2) swap(x,y);
edges.pb((ii){x,y});
}
m=Rand(200000,200000);
FOR(i,n,m){
int x=Rand(1,n);
int y=Rand(1,n);
edges.pb((ii){x,y});
}
random_shuffle(all(edges));
FOR(i,1,m){
e[i].u=edges[i-1].fs;
e[i].v=edges[i-1].sc;
e[i].w=Rand(1,3);
}
cout<<n<<" "<<m<<"\n";
cout<<S<<" "<<T<<" "<<U<<" "<<V<<"\n";
FOR(i,1,m) cout<<e[i].u<<" "<<e[i].v<<" "<<e[i].w<<"\n";
*/
cin>>n>>m;
cin>>S>>T;
cin>>U>>V;
FOR(i,1,m) cin>>e[i].u>>e[i].v>>e[i].w;
FOR(i,1,m){
int u=e[i].u,v=e[i].v,w=e[i].w;
adj[u].pb({v,w});
adj[v].pb({u,w});
}
dijkstra(0,S);
FOR(i,1,n) visited[i]=0;
dijkstra(1,U);
FOR(i,1,n) visited[i]=0;
dijkstra(2,V);
FOR(i,1,n) visited[i]=0;
queue<int> Q;
Q.push(T);
while (Q.size()){
int u=Q.front();
Q.pop();
for (ii pairs:adj[u]){
int v=pairs.fs;
int w=pairs.sc;
if (d[0][v]==d[0][u]-1LL*w){
par[u].pb(v);
child[v].pb(u);
if (!visited[v]){
Q.push(v);
visited[v]=1;
}
}
}
}
ll ans=d[1][V];
memset(f,0x3f,sizeof(f));
memset(g,0x3f,sizeof(g));
f[S]=d[1][S];
g[T]=d[2][T];
dfs(1,S);
dfs(2,T);
FOR(i,1,n) minimize(ans,f[i]+g[i]);
///
memset(f,0x3f,sizeof(f));
memset(g,0x3f,sizeof(g));
swap(S,T);
FOR(i,1,n) swap(par[i],child[i]);
f[S]=d[1][S];
g[T]=d[2][T];
dfs(1,S);
dfs(2,T);
FOR(i,1,n) minimize(ans,f[i]+g[i]);
cout<<ans;
return 0;
}
