#include <iostream>
#include <bits/stdc++.h>
using namespace std;
#define MOD 1000000007
#define MOD2 998244353
#define ll long long
#define pri pair<int,int>
#define prl pair<ll,ll>
#define vi vector<int>
#define vl vector<ll>
#define vp vector<pair<int,int>>
#define vpl vector<pair<ll,ll>>
#define re return 0
#define sqrt sqrtl
#define int ll
struct node {
vector<pri> adj;
int val;
};
int32_t main() {
int n,m;cin>>n>>m;
int s,t,u,v;cin>>s>>t>>u>>v;
vector<node> nodes(n);
for (int i = 0;i<m;i++) {
int a,b,c;cin>>a>>b>>c;
nodes[a-1].adj.push_back({b-1,c});
nodes[b-1].adj.push_back({a-1,c});
}
/* for (int i = 0;i<n;i++) {
cout<<i<<endl;
for (int j = 0;j<nodes[i].adj.size();j++) {
cout<<nodes[i].adj[j].first<<" "<<nodes[i].adj[j].second<<endl;
}
} */
auto dijkstra = [n,nodes](int start) {
vector<int> mp(n,1e18);
mp[start] = 0;
set<pri> q;
q.insert({0,start});
while (q.size()) {
auto f = *q.begin();
for (int i = 0;i<nodes[f.second].adj.size();i++) {
if (mp[nodes[f.second].adj[i].first] > (mp[f.second] + nodes[f.second].adj[i].second)) {
mp[nodes[f.second].adj[i].first] = mp[f.second] + nodes[f.second].adj[i].second;
q.insert({mp[f.second] + nodes[f.second].adj[i].second,nodes[f.second].adj[i].first});
}
}
q.erase(q.begin());
}
return mp;
};
vector<int> dijkS,dijkU,dijkV;
dijkS = dijkstra(s-1);
dijkU = dijkstra(u-1);
dijkV = dijkstra(v-1);
int disT = dijkS[t-1];
auto dfs = [disT,nodes,dijkU,dijkV,t,dijkS](int a, int prev, int length, int minX, int minY,auto&& dfs)->int {
if (length==disT && a==t-1) return minX+minY;
if (length>dijkS[a] || length>=disT) return 1e18;
int mn = 1e18;
for (int i = 0;i<nodes[a].adj.size();i++) {
if (nodes[a].adj[i].first == prev) continue;
mn = min(mn,dfs(nodes[a].adj[i].first,a,length+nodes[a].adj[i].second,min(minX,dijkU[nodes[a].adj[i].first]),min(minY,dijkV[nodes[a].adj[i].first]),dfs));
}
return mn;
};
cout<<min(dfs(s-1,-1,0,dijkU[s-1],dijkV[s-1],dfs),dijkU[v-1])<<endl;
return 0;
}
