#include <bits/stdc++.h>
#define speed ios_base::sync_with_stdio(0); cin.tie(0)
#define all(x) (x).begin(),(x).end()
#define F first
#define S second
//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx,avx2")
//#pragma GCC target("popcnt")
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ldb;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const ll MAX=2e5+10,P=1e9+7;
const ll INF=0x3f3f3f3f,oo=0x3f3f3f3f3f3f3f3f;
const ldb eps=1e-6;
const ldb PI=acos(-1.0);
const int dir[4][2]={{0,1},{0,-1},{1,0},{-1,0}};
template<typename T>
using vvector = vector<vector<T>>;
void Dijkstra(int n,vvector<pll> &G,vector<ll> &dis,ll s) {
priority_queue<pll> Q;
vector<bool> vis(n+1);
dis[s]=0;
Q.push({0,s});
while (!Q.empty()) {
while (!Q.empty() and vis[Q.top().S]) Q.pop();
if (Q.empty()) break;
auto [d,v]=Q.top();
// cout<<v<<" v\n";
vis[v]=true;
for (auto [u,w]:G[v]) {
if (vis[u]) continue;
if (dis[v]+w<dis[u]) {
dis[u]=dis[v]+w;
Q.push({-dis[u],u});
}
}
}
}
int main() {
speed;
ll n,m;
cin>>n>>m;
ll s,t,x,y;
cin>>s>>t>>x>>y;
vvector<pll> G(n+1);
for (int i=1;i<=m;i++) {
ll a,b,c;
cin>>a>>b>>c;
G[a].push_back({b,c});
G[b].push_back({a,c});
}
vector<ll> diss(n+1,oo),disx(n+1,oo),disy(n+1,oo);
Dijkstra(n,G,diss,s);
Dijkstra(n,G,disx,x);
Dijkstra(n,G,disy,y);
// for (int i=1;i<=n;i++) cout<<diss[i]<<" ";
// cout<<"diss\n";
// for (int i=1;i<=n;i++) cout<<disx[i]<<" ";
// cout<<"disx\n";
// for (int i=1;i<=n;i++) cout<<disy[i]<<" ";
// cout<<"disy\n";
vector<int> id(n+1);
iota(all(id),0);
diss[0]=-1;
sort(all(id),[&](int a,int b) {
return diss[a]<diss[b];
});
vector<ll> dpx(n+1,oo),dpy(n+1,oo),dpxy(n+1,oo);
for (int i=1;i<=n;i++) {
int v=id[i];
for (auto [u,w]:G[v]) {
if (diss[u]+w==diss[v]) {
dpx[v]=min(dpx[v],dpx[u]);
dpy[v]=min(dpy[v],dpy[u]);
dpxy[v]=min(dpxy[v],dpxy[u]);
}
}
dpx[v]=min(dpx[v],disx[v]);
dpy[v]=min(dpy[v],disy[v]);
dpxy[v]=min({dpxy[v],dpx[v]+disy[v],dpy[v]+disx[v],disx[v]+disy[v]});
}
// for (int i=1;i<=n;i++) cout<<dpx[i]<<" ";
// cout<<"dpx\n";
// for (int i=1;i<=n;i++) cout<<dpy[i]<<" ";
// cout<<"dpy\n";
// for (int i=1;i<=n;i++) cout<<dpxy[i]<<" ";
// cout<<"dpxy\n";
cout<<min(dpxy[t],disx[y])<<"\n";
return 0;
}
