#include <bits/stdc++.h>
#define ll long long
#define str string
#define ins insert
#define ld long double
#define pb push_back
#define pf push_front
#define pof pop_front()
#define pob pop_back()
#define lb lower_bound
#define ub upper_bound
#define endl "\n"
#define fr first
#define sc second
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define sz size()
#define vll vector<ll>
#define bc back()
#define arr array
#define pll vector<pair<ll,ll>>
using namespace std;
template <class _T>
bool chmin(_T &x, const _T &y){
bool f=0;
if (x>y){x=y;f=1;}
return f;
}
template <class _T>
bool chmax(_T &x, const _T &y){
bool f=0;
if (x<y){x=y;f=1;}
return f;
}
//void fre(string s){freopen((s+".in").c_str(),"r",stdin);freopen((s+".out").c_str(),"w",stdout);}
void start(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
const ll inf=1e9;
const ll mod=1e9+7;
const ll N=2e5+7;
const ld eps=1e-9;
vector<pll> g(N);
ll dp[2][N],d[N],du[N],dv[N],vis[N],ans;
void dis(ll s,ll a[]){
memset(vis,0,sizeof(vis));
set<pair<ll,ll>> st;
st.ins({0,s});
while(st.sz){
ll c,v;
tie(c,v)=*st.begin();
st.erase(st.begin());
if(vis[v])continue;
vis[v]=1;
a[v]=c;
for(auto i : g[v])st.ins({a[v]+i.sc,i.fr});
}
}
void calc(ll s,ll e){
memset(vis,0,sizeof(vis));
memset(dp,0x3f,sizeof(dp));
set<pair<ll,pair<ll,ll>>> st;
st.ins({0,{s,0}});
while(st.sz){
ll c,v,p;
pair<ll,ll> pp;
tie(c,pp)=*st.begin();
tie(v,p)=pp;
st.erase(st.begin());
if(vis[v] && c==d[v]){
if(min(dp[0][p],du[v])+min(dp[1][p],dv[v])<=dp[0][v]+dp[1][v]){
dp[0][v]=min(dp[0][p],du[v]);
dp[1][v]=min(dp[1][p],dv[v]);
}
continue;
}else if(vis[v])continue;
vis[v]=1;
d[v]=c;
dp[0][v]=min(dp[0][p],du[v]);
dp[1][v]=min(dp[1][p],dv[v]);
for(auto i : g[v])st.ins({d[v]+i.sc,{i.fr,v}});
}
chmin(ans,dp[0][e]+dp[1][e]);
}
void solve(){
ll i,j;
ll n,m,u,v,s,t;
cin>>n>>m>>s>>t>>u>>v;
ll a,b,c;
for(i=0;i<m;i++){
cin>>a>>b>>c;
g[a].pb({b,c});
g[b].pb({a,c});
}
//counting du and dv
dis(u,du);
dis(v,dv);
//simple path
ans=du[v];
//calculating dp
calc(s,t);
calc(t,s);
cout<<ans<<endl;
}
signed main(){
//start();
ll t=1;
//cin>>t;
while(t--) solve();
return 0;
}
/*
*/
