#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#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 pb push_back
#define all(x) x.begin(),x.end()
#define task "path"
#define mp make_pair
template<class x,class y>
bool minimize(x &a,const y &b){
if(a > b){
a = b;
return true;
}else return false;
}
template<class x,class y>
bool maximize(x &a,const y &b){
if(a < b){
a = b;
return true;
}else return false;
}
typedef pair<int,int> pii;
constexpr int MAXN=1e6,MOD=1e9+7,INF=1e18;
int n,m,s,t,u,v,k,l,r,ans,res;
int dist[3][MAXN];
vector<pii> adj[MAXN];
void dij1(int i,int type){
FOR(j,1,n) dist[type][j] = INF;
dist[type][i] = 0;
priority_queue<pii, vector<pii> > pq;
pq.push({0,i});
while(!pq.empty()){
int w = -pq.top().fi;
int v = pq.top().se;
pq.pop();
if(dist[type][v] != w) continue;
for(pii u : adj[v]){
if(dist[type][u.fi] > w + u.se){
dist[type][u.fi] = w + u.se;
pq.push(mp(-dist[type][u.fi],u.fi));
}
}
}
}
void dij2(int st,int e){
vector<int> dp(n+1,INF);
vector<int> miu(n+1,INF);
vector<int> miv(n+1,INF);
dp[st] = 0;
miu[st] = dist[1][st];
miv[st] = dist[2][st];
priority_queue<pii, vector<pii> > pq;
pq.push(mp(0,st));
while(!pq.empty()){
int w = -pq.top().fi;
int v = pq.top().se;
pq.pop();
if(dp[v] != w) continue;
for(pii u : adj[v]){
int newu = min(miu[v], dist[1][u.fi]);
int newv = min(miv[v], dist[2][u.fi]);
if(dp[u.fi] > w + u.se){
dp[u.fi] = w + u.se;
miu[u.fi] = newu;
miv[u.fi] = newv;
pq.push(mp(-dp[u.fi],u.fi));
}else if(dp[u.fi] == w + u.se){
if(miu[u.fi] + miv[u.fi] > newu + newv){
miu[u.fi] = newu;
miv[u.fi] = newv;
pq.push(mp(-dp[u.fi],u.fi));
}
}
if(dp[e]!=INF)
minimize(ans,miu[e]+miv[e]);
}
}
}
int32_t main(){
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
if(fopen(task".inp","r")){
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
cin >> n >> m;
cin >> s >> t >> u >> v;
FOR(i,1,m){
int u,v,w;
cin >> u >> v >> w;
adj[u].pb(mp(v,w));
adj[v].pb(mp(u,w));
}
dij1(u,1);
dij1(v,2);
ans = dist[1][v];
dij2(s,t);
dij2(t,s);
cout << ans;
return 0;
}
