#include<bits/stdc++.h>
using namespace std;
//#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//using ordered_set = tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>;
//using ordered_multiset = tree<int, null_type,less_equal<int>, rb_tree_tag,tree_order_statistics_node_update>;
//#define fbo find_by_order // use pointer, returns kth element (0-based)
//#define ook order_of_key // returns x ada di index berapa (0-based)
#define pb push_back
#define pob pop_back
#define fi first
#define se second
#define ll long long
#define ld long double
#define lll __int128
#define tp top()
#define fr front()
#define sz size()
#define rep(i,a,b) for(int i = a; i < b; ++i)
#define mem(a, b) memset(a, (b), sizeof(a))
#define clr(a) memset(a, 0, sizeof(a))
#define sqr(x) ( (x) * (x) )
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
template<typename T>
using ve = vector<T>;
using pii = pair<int,int>;
using ppi = pair<pii,int>;
using pip = pair<int,pii>;
using ppp = pair<pii,pii>;
void optIO(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
const int N = 100020;
const ll INF = 1e18;
using pll = pair<ll,ll>;
using pli = pair<pll,int>;
vector<pli> adj[N];
ll dist[N];
void dijkstra(int s, int t) {
for(int i = 0; i < N; i++) dist[i] = INF;
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({0,s});
while(pq.sz) {
ll d = pq.tp.fi;
int x = pq.tp.se;
pq.pop();
if (dist[x] <= d) continue;
dist[x] = d;
for(auto to : adj[x]) pq.push({d + to.fi.se, to.fi.fi});
}
set<pll> ms;
ms.insert({-dist[t], t});
while(ms.sz) {
auto it = *(ms.rbegin());
ms.erase(it);
int cur = it.se;
for(auto &to : adj[cur]) if (dist[to.fi.fi] + to.fi.se == dist[cur]) {
to.se = 1;
ms.insert({-dist[to.fi.fi], to.fi.fi});
}
}
}
ll dij(int s, int t) {
bool vis[N][3] = {0};
priority_queue<pli, vector<pli>, greater<pli>> pq;
pq.push({{0,s},0});
while(pq.sz) {
ll d = pq.tp.fi.fi;
ll x = pq.tp.fi.se;
int st = pq.tp.se;
pq.pop();
if (vis[x][st]) continue;
vis[x][st] = 1;
if (x == t) return d;
for(auto &to : adj[x]) {
if (st == 2) pq.push({{d + to.fi.se,to.fi.fi},2});
else if (st == 1) {
if (to.se == 1 && dist[x] == dist[to.fi.fi] + to.fi.se) pq.push({{d,to.fi.fi},1});
else pq.push({{d + to.fi.se,to.fi.fi},2});
} else {
if (to.se == 1 && dist[x] == dist[to.fi.fi] + to.fi.se) pq.push({{d,to.fi.fi},1});
pq.push({{d + to.fi.se,to.fi.fi},0});
}
}
}
return 0;
}
void solve(){
int n,m; cin>>n>>m;
int s,t; cin>>s>>t;
int u,v; cin>>u>>v;
while(m--){
int uu,vv,ww; cin>>uu>>vv>>ww;
adj[uu].pb({{vv,ww}, 0});
adj[vv].pb({{uu,ww}, 0});
}
dijkstra(s,t);
cout<<min(dij(u,v), dij(v,u))<<"\n";
}
int main() {
optIO();
// freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
int t=1;
// cin>>t;
while(t--){
solve();
}
return 0;
}
