#include <bits/stdc++.h>
using namespace std;
# define int long long
# define fir first
# define sec second
# define pb push_back
const int cnst = 2e5+5;
bool mutipletestcase = 0;
//bool debug = false;
int n, m;
int s, t, u, v;
int par[cnst];
int shor[cnst];
int parshor[cnst];
int nxtshor[cnst];
vector<pair<int, int>> vec[cnst];
void djikstrast() {
bool vis[n+5];
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq;
bool got = 0; int val = -1;
pq.push({0, s, 0}); shor[s] = shor[t] = 1;
memset(vis, 0, sizeof(vis));
while(!pq.empty()) {
auto[x, idx, parent] = pq.top(); pq.pop();
// cerr << idx << endl;
if(idx == t) got = 1, val = x;
if(got) {
if(x != val) break;
if(idx != t) continue;
idx = parent;
while(par[idx] != 0) {
shor[idx] = 1;
nxtshor[par[idx]] = idx;
parshor[idx] = par[idx];
idx = par[idx];
}
continue;
}
if(vis[idx]) continue;
vis[idx] = 1;
par[idx] = parent;
for(auto v: vec[idx]) {
if(!vis[v.fir]) pq.push({x+v.sec, v.fir, idx});
}
}
// for(int i = 1; i<=n; i++) cerr << shor[i] << " "; cerr << endl;
}
void djikstrauv() {
bool vis[n+5][5];
memset(vis, 0, sizeof(vis));
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq;
pq.push({0, u, 0});
if(shor[u]) pq.push({0, u, 1}), pq.push({0, u, 2});
while(!pq.empty()) {
auto[x, idx, id] = pq.top(); pq.pop();
if(vis[idx][id]) continue;
vis[idx][id] = 1;
// cerr << x << " " << idx << " " << id << endl;
if(idx == v) {
cout << x << endl; return;
}
if(id == 0) {
for(auto v: vec[idx]) {
if(!vis[v.fir][0]) pq.push({x+v.sec, v.fir, 0});
if(shor[v.fir]) {
if(!vis[v.fir][1]) pq.push({x+v.sec, v.fir, 1});
if(!vis[v.fir][2]) pq.push({x+v.sec, v.fir, 2});
}
}
}
else if(id == 1) {
int y = parshor[idx];
if(!vis[y][1]) pq.push({x, y, 1});
for(auto v: vec[idx]) if(!vis[v.fir][3]) pq.push({x+v.sec, v.fir, 3});
}
else if(id ==2) {
int y = nxtshor[idx];
if(!vis[y][2]) pq.push({x, y, 2});
for(auto v: vec[idx]) {
if(!vis[v.fir][3]) pq.push({x+v.sec, v.fir, 3});
}
}
else {
for(auto v: vec[idx]) if(!vis[v.fir][3]) pq.push({x+v.sec, v.fir, 3});
}
}
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i<=m; i++) {
int a, b, c; cin >> a >> b >> c;
vec[a].pb({b, c});
vec[b].pb({a, c});
}
djikstrast();
djikstrauv();
}
signed main() {
ios_base::sync_with_stdio(false);
int t = 1;
if(mutipletestcase) cin >> t;
while(t--) solve();
}
