//
#include <bits/stdc++.h>
using namespace std;
#define int long long
int MOD = 1000000007;
void solve(){
int n, m; // node, edge
int s, t; // start and end commuter pass
int u, v; // start and end
cin >> n >> m >> s >> t >> u >> v;
vector<pair<int, int> > adj[n + 3];
for(int i = 0; i < m; i++){
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<int> scp(n + 5, -1); // c-pass dari s
vector<int> tcp(n + 5, -1); // c-pass dari t
priority_queue<pair<int, int> > pq;
pq.push({0, s});
// cari scp, pake minus karna dijkstra
while(!pq.empty()){
int cost = - pq.top().first;
int nd = pq.top().second;
pq.pop();
if(scp[nd] != -1) continue;
scp[nd] = cost;
for(auto x : adj[nd]){
if(scp[x.first] == -1){
pq.push({-(cost + x.second), x.first});
}
}
}
pq.push({0, t});
while(!pq.empty()){
int cost = - pq.top().first;
int nd = pq.top().second;
pq.pop();
if(tcp[nd] != -1) continue;
tcp[nd] = cost;
for(auto x : adj[nd]){
if(tcp[x.first] == -1){
pq.push({-(cost + x.second), x.first});
}
}
}
int len = scp[t];
// cout << len << endl;
// conditions
// 0 -> dijkstra biasa
// 1 -> gunakan c-pass s -> t
// 2 -> gunakan c-pass t -> S
// 3 -> habis c-pass, menuju v
// cost ga berubah di 1 dan 2
priority_queue<tuple<int, int, int> > dj; // dist, nd, conditions
dj.push({0, u, 0});
int dis[n + 3][4];
memset(dis, -1, sizeof dis);
while(!dj.empty()){
// cout << "e" << endl;
int cost = - get<0>(dj.top());
int nd = get<1>(dj.top());
int c = get<2>(dj.top());
dj.pop();
if(dis[nd][c] != -1){
continue;
}
dis[nd][c] = cost;
if(c == 0){
// lanjutttt di c = 0
for(auto x : adj[nd]){
if(dis[x.first][c] == -1){
dj.push({-(cost + x.second), x.first, 0});
}
}
// c => 1
for(auto x : adj[nd]){
if(scp[nd] + tcp[x.first] + x.second == len && dis[x.first][1] == -1){
dj.push({-cost, x.first, 1});
}
}
// c => 2
for(auto x : adj[nd]){
if(tcp[nd] + scp[x.first] + x.second == len && dis[x.first][2] == -1){
dj.push({-cost, x.first, 2});
}
}
}
else if(c == 1){
// lanjut di c = 1
for(auto x : adj[nd]){
if(scp[nd] + tcp[x.first] + x.second == len && dis[x.first][1] == -1){
dj.push({-cost, x.first, 1});
}
}
// c => 3
for(auto x : adj[nd]){
if(dis[x.first][3] == -1){
dj.push({-(cost + x.second), x.first, 3});
}
}
}
else if(c == 2){
// lanjut di c = 2
for(auto x : adj[nd]){
if(tcp[nd] + scp[x.first] + x.second == len && dis[x.first][2] == -1){
dj.push({-cost, x.first, 2});
}
}
// c => 3
for(auto x : adj[nd]){
if(dis[x.first][3] == -1){
dj.push({-(cost + x.second), x.first, 3});
}
}
}
else{
for(auto x : adj[nd]){
if(dis[x.first][c] == -1){
dj.push({-(cost + x.second), x.first, 3});
}
}
}
}
// int ans = dis[v][0];
// ans = min(ans , dis[v][1]);
// ans = min(ans , dis[v][2]);
// ans = min(ans , dis[v][3]);
// cout << ans << endl;
int ans = 1e15;
for(int i = 0; i < 4; i++){
if(dis[v][i] != -1){
ans = min(ans, dis[v][i]);
}
// cout << dis[v][i] << endl;
}
cout << ans << endl;
}
signed main(){
int t;
t = 1;
for(int i = 1; i<=t; i++){
solve();
}
}
