#include <bits/stdc++.h>
using namespace std;
#define sz(arr) ((int) arr.size())
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef pair<ll, ll> pll;
typedef vector<pll> vll;
const int INF = 1e9;
const ll INFL = 1e18;
const int MOD = 1e9+7;
const double EPS = 1e-9;
int dirx[4] = {0,-1,1,0};
int diry[4] = {-1,0,0,1};
int dr[] = {1, 1, 0, -1, -1, -1, 0, 1};
int dc[] = {0, 1, 1, 1, 0, -1, -1, -1};
const string ABC = "abcdefghijklmnopqrstuvwxyz";
const char ln = '\n';
map<ii, bool> marked;
ll dijkstra(vector<vll> &adj, int s, int V, int t, vi &parent){
vl dist(V+1, INFL); dist[s] = 0;
priority_queue<pll, vll, greater<pll> > pq; pq.push(pll(0LL, s));
while(!pq.empty()){
pll front = pq.top(); pq.pop();
ll d = front.first, u = front.second;
if (d > dist[u]) continue;
for (int j = 0; j < (int)adj[u].size(); j++){
pll v = adj[u][j];
if (marked[{u, v.first}]) v.second = 0LL;
if (dist[u] + v.second < dist[v.first]){
dist[v.first] = dist[u] + v.second;
parent[v.first] = u;
pq.push(pll(dist[v.first], v.first));
}
}
}
return dist[t];
}
void path(vi &p, int s, int t, vi &ans){
if (s == t) {ans.push_back(t); return;}
path(p, s, p[t], ans);
ans.push_back(t);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(20) << fixed;
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
vector<vll> adj(n+1);
for (int i = 0; i<m; i++){
ll a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vi p(n+1, -1);
dijkstra(adj, s, n, t, p);
vi camino;
path(p, s, t, camino);
for (int i = 0; i<sz(camino)-1; i++) {
marked[{camino[i], camino[i+1]}] = true;
marked[{camino[i+1], camino[i]}] = true;
}
cout << dijkstra(adj, u, n, v, p) << ln;
return 0;
}
