#include <bits/stdc++.h>
typedef long long int ll;
#define INF ll(1e18 + 7)
#define N (ll)1e5 + 5
using namespace std;
#define int ll
int n, m, s, t, u2, v, g, h, z, g2, h2;
vector<pair<int, int>> v2[N];
bool used[N];
int ds[N], du[N], dv[N];
pair<int, int> d1[N], d2[N];
void bfs(){
memset(used, 0, sizeof(used));
priority_queue<pair<int, int>> q;
q.push({0, s});
pair<int, int> p;
while(!q.empty()){
p = q.top();
q.pop();
if(used[p.second])continue;
used[p.second] = 1;
for(auto u : v2[p.second]){
if(!used[u.first] && ds[u.first] > ds[p.second] + u.second){
ds[u.first] = ds[p.second] + u.second;
q.push({-ds[u.first], u.first});
}
}
}
}
void bfs2(){
memset(used, 0, sizeof(used));
priority_queue<pair<int, int>> q;
q.push({0, u2});
pair<int, int> p;
while(!q.empty()){
p = q.top();
q.pop();
if(used[p.second])continue;
used[p.second] = 1;
for(auto u : v2[p.second]){
if(!used[u.first] && du[u.first] > du[p.second] + u.second){
du[u.first] = du[p.second] + u.second;
q.push({-du[u.first], u.first});
}
}
}
}
void bfs3(){
memset(used, 0, sizeof(used));
priority_queue<pair<int, int>> q;
q.push({0, v});
pair<int, int> p;
while(!q.empty()){
p = q.top();
q.pop();
if(used[p.second])continue;
used[p.second] = 1;
for(auto u : v2[p.second]){
if(!used[u.first] && dv[u.first] > dv[p.second] + u.second){
dv[u.first] = dv[p.second] + u.second;
q.push({-dv[u.first], u.first});
}
}
}
}
void solve(){
cin >> n >> m >> s >> t >> u2 >> v;
for(int i=0; i<m; i++){
cin >> g >> h >> z;
v2[g].push_back({h, z});
v2[h].push_back({g, z});
}
fill(ds, ds+n+1, INF);
fill(du, du+n+1, INF);
fill(dv, dv+n+1, INF);
fill(d1, d1 + n + 1, make_pair(INF, INF));
fill(d2, d2 + n + 1, make_pair(INF, INF));
ds[s] = du[u2] = dv[v] = 0;
bfs();
bfs2();
bfs3();
for(int i=1; i<=n; i++){
d1[i] = d2[i] = {du[i], dv[i]};
}
int t1, t2, t3, t4;
memset(used, 0, sizeof(used));
priority_queue<pair<int, int>> q;
q.push({0, s});
pair<int, int> p;
while(!q.empty()){
p = q.top();
q.pop();
if(used[p.second])continue;
used[p.second] = 1;
g = d1[p.second].first, g2= d1[p.second].second, h = d2[p.second].first, h2= d2[p.second].second;
for(auto u : v2[p.second]){
if(ds[u.first] == ds[p.second] + u.second){
t1 = min(g, du[u.first]);
t2 = min(g2, dv[u.first]);
t3 = min(h, du[u.first]);
t4 = min(h2, dv[u.first]);
d1[u.first] = {t1, t2};
d2[u.first] = {t3, t4};
q.push({-ds[u.first], u.first});
}
}
}
cout<< min(min(d1[t].first + d1[t].second, d2[t].first + d2[t].second), du[v]);
}
signed main(){
//freopen("shortcut.in", "r", stdin);
//freopen("shortcut.out", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
int T = 1;
//cin>>T;
while (T--){
solve();
}
}
