#include <bits/stdc++.h>
#define int long long
#define debug(u) cerr<<(u == inf ? "inf" : to_string(u))<<endl
#define int long long
using namespace std;
using namespace chrono;
const int mxn = 100005;
const int inf = 1e18;
const int LOG = 17;
int n,m,s,t,u,v;
vector<pair<int,int> > g[mxn];
void dijk(int x, vector<int>&dis){
priority_queue<pair<int,int> > pq;
dis[x] = 0;
pq.push({0,x});
while(pq.size()){
int x = (pq.top()).second;
pq.pop();
for(auto p : g[x]){
if(dis[p.first] > dis[x] +p.second){
dis[p.first] = dis[x] + p.second;
pq.push({-dis[p.first],p.first});
}
}
}
}
void solve(int T){
cin >> n >> m >> s >> t >> u >> v;
while(m--){
int x, y, w;
cin >> x >> y >> w;
g[x].push_back({y, w});
g[y].push_back({x, w});
}
vector<int> disu(n+1, 1e17), disv(n+1, 1e17), dis(n+1, 1e17), canu(n+1, 1e17), canv(n+1, 1e17);
dijk(v, disv); dijk(u, disu);
vector<bool> vis(n+1, 0);
priority_queue<pair<pair<int,int>,int>, vector<pair<pair<int,int>,int>>, greater<pair<pair<int,int>,int>>> q;
q.push({{0, s}, 0});
dis[s] = 0;
while(!q.empty()){
int w = q.top().first.first;
int x = q.top().first.second, pr = q.top().second;
q.pop();
if (w != dis[x]) continue;
if (min(disv[x], canv[pr])+min(disu[x], canu[pr]) < canu[x]+canv[x]){
canv[x] = min(disv[x], canv[pr]);
canu[x] = min(disu[x], canu[pr]);
}
if (vis[x]) continue;
vis[x] = 1;
for (auto i : g[x]){
if (dis[i.first] >= dis[x]+i.second){
dis[i.first] = dis[x]+i.second;
q.push({{dis[i.first], i.first}, x});
}
}
}
cout << min(canu[t]+canv[t], disv[u]);
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t = 1;
//cin>>t;
for(int i = 1;i<=t;i++){
solve(i);
}
}
