#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define all(c) c.begin(), c.end()
#define endl "\n"
const double PI=3.141592653589;
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define dbg(x...) cerr << "LINE(" << __LINE__ << ") -> " <<"[" << #x << "] = ["; _print(x)
#else
#define dbg(x...)
#endif
int n,m;
vector<vector<int>>nadj;
vector<vector<pair<int,int>>>adj;
int res;
vector<int> dij(int s){
vector<int>dist(n+1,1e18);
dist[s] = 0;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,s});
while(!pq.empty()){
int d = pq.top().first, u = pq.top().second;
pq.pop();
if(dist[u]!=d)continue;
for(auto &[v,c] : adj[u]){
int cur_dist = dist[v], new_dist = dist[u]+c;
if(new_dist < cur_dist){
dist[v] = new_dist;
pq.push({new_dist, v});
}
}
}
return dist;
}
vector<int>dists,distt,distu,distv;
void solve()
{
cin >> n >> m;
adj.resize(n+1);
nadj.resize(n+1);
int s,t,u,v;
cin >> s >> t >> u >> v;
for(int i = 1;i<=m;++i){
int u,v,c;
cin >> u >> v >> c;
adj[u].pb({v,c});
adj[v].pb({u,c});
}
dists = dij(s);
distt = dij(t);
distu = dij(u);
distv = dij(v);
vector<int>deg(n+1);
for(int i =1;i<=n;++i){
for(auto &[v,c] : adj[i]){
// check if edge i->v (directed) lies on shortest path from s->t
if(dists[i]+c+distt[v] == dists[t]){
nadj[i].pb(v);
deg[v]++;
}
}
}
res = distu[v];
queue<int>q;
q.push(s);
vector<int>vis(n+1),dp1(n+1),dp2(n+1);
// dp1[i] min distance from u uptill node i
// dp2[i] min distance from v uptill node i
for(int i = 1;i<=n;++i){
dp1[i] = distu[i];
dp2[i] = distv[i];
}
while(!q.empty()){
int u = q.front();
q.pop();
if(vis[u])continue;
vis[u] = 1;
for(int v : nadj[u]){
deg[v]--;
if((dp1[u]+dp2[u]) <= (dp1[v]+dp2[v])){
dp1[v] = min(dp1[u],dp1[v]);
dp2[v] = min(dp2[u],dp2[v]);
}
if(deg[v]==0)q.push(v);
}
}
for(int i = 1;i<=n;++i){
if(vis[i])res = min(res, dp1[i]+dp2[i]);
}
cout << res << endl;
}
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
// freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
int T=1;
for(int i = 1;i<=T;++i)
{
// cout << "Case #" << i << ": ";
solve();
}
}
