#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template <typename T>
using indexed_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define int long long
#define pb push_back
#define pf push_front
#define eb emplace_back
#define ins insert
#define F first
#define S second
#define MAXN 100005
#define LOG (int)log2(MAXN)+1
const int INF = 1e18;
const int MOD = 998244353;
const double EPS = 1e-8;
//15 p.
int N, M, S, T, U, V;
vector<vector<pair<int, int>>> g;
int d1[MAXN], d2[MAXN], dist[MAXN];
vector<tuple<int, int, int>> edges;
map<pair<int, int>, bool> used;
void init(){
g.resize(N+1);
fill(d1, d1+MAXN, INF);
fill(d2, d2+MAXN, INF);
fill(dist, dist+MAXN, INF);
}
void dijkstra1(){
set<pair<int, int>> q;
q.ins({d1[S]=0, S});
int u, w;
while(!q.empty()){
tie(w, u) = *q.begin();
q.erase(q.begin());
for(auto&[to, W]:g[u]){
if(w+W<d1[to]){
d1[to] = w+W;
q.ins({d1[to], to});
}
}
}
int dist = d1[T];
q.ins({d2[T] = 0, T});
while(!q.empty()){
tie(w, u) = *q.begin();
q.erase(q.begin());
for(auto&[to, W]:g[u]){
if(w+W<d2[to]){
d2[to] = w+W;
q.ins({d2[to], to});
}
}
}
int v;
for(int i = 0; i < edges.size(); i++){
tie(u, v, w) = edges[i];
if(d1[u]+d2[v]+w==dist){
used[{u, v}] = 1;
used[{v, u}] = 1;
}
}
}
void dijkstra2(){
set<pair<int, int>> q;
q.ins({dist[U] = 0, U});
int u, w;
while(!q.empty()){
tie(w, u) = *q.begin();
q.erase(q.begin());
for(auto&[to, W]:g[u]){
int tW = (used[{u, to}]?0: W);
if(w+tW<dist[to]){
dist[to] = w+tW;
q.ins({dist[to], to});
}
}
}
}
void solve() {
cin >> N >> M >> S >>T >> U >> V;
init();
for(int i = 0; i < M; i++){
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
edges.pb({u, v, w});
edges.pb({v, u, w});
}
dijkstra1();
dijkstra2();
cout << dist[V] << '\n';
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int t = 1;
//cin >> t;
while(t--) solve();
return 0;
}
