#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = long long;
const int N = 1e5 + 99;
vector<pair<int,ll>>tab[N];
const ll inf = 1e18;
ll odl[N];
ll dijkstra(int a, int b, int n){
for(int i = 0; i < n+ 9; ++i)odl[i] = inf;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
pq.push({0,a});
while(!pq.empty()){
auto[x,v] = pq.top();
pq.pop();
if(odl[v] <= x)continue;
odl[v] = x;
for(auto [u,y] : tab[v]){
pq.push({x+y,u});
}
}
return odl[b];
}
ll odl2[N][3];
int S,T, U, V;
map<pair<int,int>,int>Star;
ll dijkstra2(int a,int b,int n){
for(int i = 0; i < n + 9; i++){
odl2[i][0] = odl2[i][1] = odl2[i][2] = inf;
}
priority_queue<pair<ll,pair<int,int>>, vector<pair<ll,pair<int,int>>>, greater<pair<ll,pair<int,int>>>> pq;
pq.push({0,{a,0}});
while(!pq.empty()){
auto[x, p1] = pq.top();
pq.pop();
auto[v, l] = p1;
if(l > 2)continue;
// if(v == 2 && l == 0){
// cout << "Xd" << x << endl;
// }
if(odl2[v][l] <= x)continue;
odl2[v][l] = x;
for(auto [u,w] : tab[v]){
// if(v == 2 && u == 4){
// cout << "x + STar[{u,v}]" << " " << x + Star[{u,v}] << endl;
// cout << x << " " << " lol " << Star[{u,v}] << endl;
// }
pq.push({x+Star[{u,v}],{u,l}});
if(l == 0){
if(w == 0)pq.push({x,{u,1}});
else pq.push({x+w,{u,0}});
}
else if(l == 1){
if(w == 0 && v != T)pq.push({x,{u,1}});
}
}
}
return min(min(odl2[b][1],odl2[b][0]),odl2[b][2]);
}
bool vis[N];
map<pair<int,int>,bool>M;
void dfs(int v, ll x){
assert(odl[v] == x);
if(x == 0)return;
if(vis[v])return;
vis[v] = 1;
ll mini = inf;
for(auto [u,y] : tab[v]){
mini = min(mini, odl[u] + y);
}
for(auto [u, y] : tab[v]){
if(mini == odl[u] + y){
dfs(u,x - y);
M[{v,u}]=1;
// M[{u,v}]=1;
}
}
}
int main(){
int n, m;
cin >> n >> m;
cin >> S >> T >> U >> V;
for(int i = 0; i < m; i++){
int a, b, c;
cin >> a >> b >> c;
tab[a].push_back({b,c});
Star[{a,b}] = c;
Star[{b,a}] = c;
tab[b].push_back({a,c});
}
ll oo = dijkstra(S,T,n);
dfs(T,oo);
for(int i = 1; i <= n; i++){
for(auto &[v,x] : tab[i]){
if(M[{i,v}])x = 0;
else x = Star[{i,v}];
}
}
ll ooo = dijkstra2(U,V,n);
for(int i = 1; i <= n; i++){
for(auto &[v,x] : tab[i]){
if(M[{v,i}])x = 0;
else x = Star[{i,v}];
}
}
swap(S,T);
ll oooo = dijkstra2(U,V, n);
cout << min(ooo,oooo) << endl;
}
