#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
using namespace std;
using ll = long long;
ll n,m,s,t,u,v;
ll ans;
vector<vector<pair<ll,ll>>> neigh;
unordered_map<ll, unordered_map<ll,ll>> dist;
vector<vector<ll>> parents;
vector<vector<ll>> kids;
vector<bool> important;
vector<ll> ds;
vector<ll> du;
vector<ll> dv;
vector<ll> dt;
vector<ll> dp_u;
vector<ll> dp_v;
void djkstra1(ll st, ll en){
vector<bool> visited;
vector<vector<int>> came_from;
visited.assign(n,0);
came_from.resize(n);
important.assign(n,0);
priority_queue<array<ll,3>, vector<array<ll,3>>, greater<array<ll,3>>> tasks;
//tasks.push({0,st,st});
ds[st] = 0;
for(pair<ll,ll> go:neigh[st]){
tasks.push({go.se, go.fi, st});
}
while(!tasks.empty()){
ll c = (tasks.top())[0];
ll tar = (tasks.top())[1];
ll fro = (tasks.top())[2];
tasks.pop();
if(ds[tar] == LLONG_MAX){
ds[tar] = c;
came_from[tar].pb(fro);
parents[tar].pb(fro);
kids[fro].pb(tar);
}else if(c == ds[tar]){
came_from[tar].pb(fro);
parents[tar].pb(fro);
kids[fro].pb(tar);
}
if(visited[tar]){continue;}
for(pair<ll,ll> go:neigh[tar]){
tasks.push({c+go.se, go.fi, tar});
}
visited[tar] = 1;
}
important[en] = 1;
queue<ll> valuables;
valuables.push(en);
while(!valuables.empty()){
ll curr = valuables.front();
valuables.pop();
for(ll a:parents[curr]){
if(important[a] == 0){
//this is unnecessary
if(ds[a]+dist[a][curr] == ds[curr]){
important[a] = 1; valuables.push(a);
}
}
}
}
/*
for(ll i=0; i<n; i++){
cout << "imp " << i+1 << " " << important[i] << endl;
}
*/
for(ll i=0; i<n; i++){
if(important[i] == 0){
parents[i].clear();
kids[i].clear();
}
vector<ll> psd;
for(int a:parents[i]){
if(important[a]){psd.pb(a);}
}
parents[i] = psd;
psd.clear();
for(int a:kids[i]){
if(important[a]){psd.pb(a);}
}
kids[i] = psd;
}
/*
for(ll i=0; i<n; i++){
cout << i+1 << ": ";
for(ll go:kids[i]){
cout << go+1 << " ";
}
cout << endl;
}
*/
}
void djkstra2(vector<ll> &vec, ll st){
priority_queue<array<ll,3>, vector<array<ll,3>>, greater<array<ll,3>>> tasks;
vector<ll> visited;
visited.assign(n,0);
vec[st] = 0;
visited[st] = 1;
for(pair<ll,ll> a:neigh[st]){
tasks.push({a.se, a.fi, st});
}
while(!tasks.empty()){
ll c = tasks.top()[0];
ll tar = tasks.top()[1];
ll fro = tasks.top()[2];
tasks.pop();
if(visited[tar]){continue;}
visited[tar] = 1;
vec[tar] = c;
for(pair<ll,ll> go:neigh[tar]){
tasks.push({c+go.se, go.fi});
}
}
}
inline void calc_dp_u(ll node){
dp_u[node] = min<ll>(du[node],dp_u[node]);
for(ll p:parents[node]){
dp_u[node] = min<ll>(dp_u[p], dp_u[node]);
}
for(ll go:kids[node]){
calc_dp_u(go);
}
}
inline void calc_dp_v(ll node){
dp_v[node] = min<ll>(dv[node],dp_v[node]);
for(ll p:kids[node]){
dp_v[node] = min<ll>(dp_v[p], dp_v[node]);
}
for(ll go:parents[node]){
calc_dp_v(go);
}
}
void dfs(ll node, ll &psd_ans){
//maybe a protection against llong_max sum
psd_ans = min<ll>(dp_u[node]+dp_v[node], psd_ans);
for(ll go:kids[node]){dfs(go, psd_ans);}
}
ll solve(){
ds.clear();
ds.assign(n, LLONG_MAX);
dt.clear();
dt.assign(n, LLONG_MAX);
du.clear();
du.assign(n, LLONG_MAX);
dv.clear();
dv.assign(n, LLONG_MAX);
dp_u.clear();
dp_u.assign(n, LLONG_MAX);
dp_v.clear();
dp_v.assign(n, LLONG_MAX);
parents.clear();
parents.resize(n);
kids.clear();
kids.resize(n);
important.clear();
important.assign(n,0);
djkstra1(s,t);
djkstra2(du, u);
djkstra2(dv, v);
djkstra2(dt, t);
calc_dp_u(s);
calc_dp_v(t);
ll psd_ans = LLONG_MAX;
dfs(s, psd_ans);
return psd_ans;
return 0;
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(NULL);
//freopen("input.txt","r",stdin);
//freopen("output.txt","w",stdout);
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
neigh.resize(n);
parents.resize(n);
kids.resize(n);
ds.assign(n, LLONG_MAX);
for(ll i=0; i<m; i++){
ll n1,n2,c;
cin >> n1 >> n2 >> c;
n1--; n2--;
neigh[n1].pb({n2,c});
neigh[n2].pb({n1,c});
dist[n1][n2] = c;
dist[n2][n1] = c;
}
ans = solve();
/*
for(ll i=0; i<n; i++){
cout << i+1 << ": ";
for(int a:kids[i]){
cout << a+1 << " ";
}
cout << endl;
}
*/
ll psd;
/*
psd = s;
s = t;
t = psd;
*/
psd = u;
u = v;
v = psd;
ans = min<ll>(ans, solve());
ans = min<ll>(ans, du[v]);
cout << ans << endl;
}
