#include <bits/stdc++.h>
#define int long long
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define last(a) a[sz(a)-1]
using namespace std;
vector<vector<pair<int,int>>> neigh;
vector<pair<int,int>> two_dist;
int N,M,S,T,U,V;
int MAXDIST=0;
void setup_twodist(){
vector<pair<int,int>> visited(N,{false,false});
priority_queue<pair<int,int>> pq;
pq.push({0,S});
two_dist[S].first=0;
while(!pq.empty()){
int x=pq.top().second; pq.pop();
if(visited[x].first) continue;
visited[x].first=true;
for (auto u : neigh[x])
{
if(two_dist[u.first].first>two_dist[x].first+u.second){
two_dist[u.first].first=two_dist[x].first+u.second;
pq.push({-two_dist[u.first].first, u.first});
}
}
}
pq.push({0,T});
two_dist[T].second=0;
while(!pq.empty()){
int x=pq.top().second; pq.pop();
if(visited[x].second) continue;
visited[x].second=true;
for (auto u : neigh[x])
{
if(two_dist[u.first].second>two_dist[x].second+u.second){
two_dist[u.first].second=two_dist[x].second+u.second;
pq.push({-two_dist[u.first].second, u.first});
}
}
}
MAXDIST=two_dist[T].first;
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr);
cin >> N >> M >> S >> T >> U >> V; S--; T--; U--; V--;
neigh.resize(N);
two_dist.resize(N,{1e17,1e17});
for (int i = 0; i < M; i++)
{
int a,b,c; cin >> a >> b >> c;
neigh[a-1].push_back({b-1,c});
neigh[b-1].push_back({a-1,c});
}
setup_twodist();
vector<vector<vector<bool>>> visited(N,vector<vector<bool>>(3,vector<bool>(3,false))); // [x][direction(or none)][never been on - is on - is off]
vector<vector<vector<int>>> dist(N,vector<vector<int>>(3,vector<int>(3,1e17))); // [x][direction(or none)][never been on - is on - is off]
priority_queue<pair<int,pair<int,pair<int,int>>>> pq;
pq.push({0,{U,{0,0}}});
dist[U][0][0]=0;
if(two_dist[U].first+two_dist[U].second==MAXDIST){ dist[U][0][1]=0; pq.push({0,{U,{0,1}}}); }
while(!pq.empty()){
int x=pq.top().second.first; int dir=pq.top().second.second.first; int used=pq.top().second.second.second; pq.pop();
if(visited[x][dir][used]) continue;
visited[x][dir][used]=true;
for (auto u : neigh[x])
{
int nd=0,nu=0;
if(used==0){
// get off
nd=0;
nu=0;
if(dist[u.first][nd][nu]>dist[x][dir][used]+u.second){
dist[u.first][nd][nu]=dist[x][dir][used]+u.second;
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
// get on
if(two_dist[u.first].first+two_dist[u.first].second==MAXDIST){
nd=0;
nu=1;
if(dist[u.first][nd][nu]>dist[x][dir][used]+u.second){
dist[u.first][nd][nu]=dist[x][dir][used]+u.second;
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
}
} else if(used==1){
// get off
nd=0;
nu=2;
if(dist[u.first][nd][nu]>dist[x][dir][used]+u.second){
dist[u.first][nd][nu]=dist[x][dir][used]+u.second;
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
if(two_dist[u.first].first+two_dist[u.first].second==MAXDIST){
// continue
if(dir==1||dir==0){
if(two_dist[x].first-u.second==two_dist[u.first].first&&two_dist[x].second+u.second==two_dist[u.first].second){
nd=1; nu=1;
if(dist[u.first][nd][nu]>dist[x][dir][used]) {
dist[u.first][nd][nu]=dist[x][dir][used];
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
}
}if(dir==2||dir==0){
if(two_dist[x].first+u.second==two_dist[u.first].first&&two_dist[x].second-u.second==two_dist[u.first].second){
nd=2; nu=1;
if(dist[u.first][nd][nu]>dist[x][dir][used]) {
dist[u.first][nd][nu]=dist[x][dir][used];
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
}
}
}
} else if(used==2){
nd=2;
nu=2;
if(dist[u.first][nd][nu]>dist[x][dir][used]+u.second){
dist[u.first][nd][nu]=dist[x][dir][used]+u.second;
pq.push({-dist[u.first][nd][nu],{u.first,{nd,nu}}});
}
}
}
}
int mn=1e17;
for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { mn=min(dist[V][i][j],mn); } }
cout << mn << "\n";
return 0;
}
