#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <set>
#include <iterator>
#include <stack>
#include <map>
#include <math.h>
#include <bitset>
#include <deque>
#include <string>
#include <tuple>
#include <queue>
#include <numeric>
#include <complex>
#include <assert.h>
#include <unordered_set>
#include <unordered_map>
#define ll long long
#define ld long long double
#define rep(i, a, b) for (long long i = a; i <= b; i++)
#define mod 1000000007ll
#define INF 1e18
#define pb push_back
#define ff first
#define ss second
#define endl '\n'
#define all(x) (x).begin (), (x).end ()
#define sz(x) (ll) (x).size ()
#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())
#define rank rnk
#define log lg
#define fast \
ios_base::sync_with_stdio (false); \
cin.tie (NULL); \
cout.tie (NULL)
using namespace std;
vector <pair<ll,ll>> adj[100000+1];
vector <ll> du(1e5+1,INF), dv(1e5+1,INF);
void getdist(ll source, vector <ll> &d)
{
set<pair<ll,ll>> s;
s.insert({0,source});
d[source]=0;
while(!s.empty())
{
auto v=*s.rbegin();
s.erase(v);
for(auto u:adj[v.ss])
if(d[u.ff]>v.ff+u.ss)
{
s.erase({d[u.ff],u.ff});
d[u.ff]=v.ff+u.ss;
s.insert({d[u.ff],u.ff});
}
}
}
signed main()
{
fast;
// freopen("curling.in","r",stdin);
// freopen("curling.out","w",stdout);
ll n,m;
cin>>n>>m;
ll s,t,u,v;
cin>>s>>t>>u>>v;
rep(i,1,m)
{
ll a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
getdist(u,du);
getdist(v,dv);
// rep(i,1,n)
// cout<<du[i]<<" "<<dv[i]<<endl;
set <pair<ll,ll>> st;
vector <ll> d(n+1,INF);
vector <ll> mindu(n+1);
vector <ll> myscoreu(n+1);
vector <ll> bestscoreu(n+1);
vector <ll> mindv(n+1), myscorev(n+1), bestscorev(n+1);
d[s]=0;
mindu[s]=du[s];
mindv[s]=dv[s];
myscoreu[s]=myscorev[s]=bestscoreu[s]=bestscorev[s]=d[u]+dv[s];
st.insert({0,s});
while(!st.empty())
{
auto [dist, vertex]=*st.rbegin();
st.erase({dist,vertex});
for(auto u:adj[vertex])
{
if(d[u.ff]>dist+u.ss)
{
st.erase({d[u.ff],u.ff});
d[u.ff]=dist+u.ss;
st.insert({d[u.ff],u.ff});
mindu[u.ff]=min(du[u.ff],mindu[vertex]);
myscoreu[u.ff]=dv[u.ff]+mindu[u.ff];
bestscoreu[u.ff]=min(myscoreu[u.ff],bestscoreu[vertex]);
mindv[u.ff]=min(dv[u.ff],mindv[vertex]);
myscorev[u.ff]=du[u.ff]+mindv[u.ff];
bestscorev[u.ff]=min(myscorev[u.ff],bestscorev[vertex]);
}
// else if(d[u.ff]==dist+u.ss)
// {
// st.insert({d[u.ff],u.ff});
// mindu[u.ff]=min({mindu[u.ff],mindu[vertex],du[u.ff]});
// myscoreu[u.ff]=min(myscoreu[u.ff], dv[u.ff]+mindu[u.ff]);
// bestscoreu[u.ff]=min({myscoreu[u.ff], bestscoreu[vertex], bestscoreu[u.ff]});
// mindv[u.ff]=min({mindv[u.ff],mindv[vertex],dv[u.ff]});
// myscorev[u.ff]=min(myscorev[u.ff], du[u.ff]+mindv[u.ff]);
// bestscorev[u.ff]=min({myscorev[u.ff], bestscorev[vertex], bestscorev[u.ff]});
// }
}
}
cout<<min(bestscoreu[t], bestscorev[t])<<endl;
return 0;
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
8 8
5 7
6 8
1 2 2
2 3 3
3 4 4
1 4 1
1 5 5
2 6 6
3 7 7
4 8 8
5 5
1 5
2 3
1 2 1
2 3 10
2 4 10
3 5 10
4 5 10
*/
