/*
OJUZ commuter pass
if sps[i] + spt[i] == sps[t]:
can be in sp
convert this to DAG
dp on DAG
dp[i][0] -> minimize x
dp[i][1] -> minimize y
*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll BIG = 1e18;
vector<ll> shortest_paths(ll n, vector<vector<pair<ll, ll>>> &adj){
vector<ll> res(adj.size(), LLONG_MAX);
res[n] = 0;
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
pq.push({0, n});
while(!pq.empty()){
auto [dist, c] = pq.top();
pq.pop();
if(res[c] != dist) continue;
for(pair<ll, ll> e:adj[c]){
if(res[e.first] > dist + e.second){
res[e.first] = dist + e.second;
pq.push({res[e.first], e.first});
}
}
}
return res;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
ll n,m;cin>>n>>m;
ll s,t;cin>>s>>t;
ll u,v;cin>>u>>v;
s--,t--,u--,v--;
vector<vector<pair<ll, ll>>> adj(n);
for(ll i=0;i<m;i++){
ll a,b,c;cin>>a>>b>>c;a--,b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<ll> sps(n),spt(n),spu(n),spv(n);
sps = shortest_paths(s, adj);
spt = shortest_paths(t, adj);
spu = shortest_paths(u, adj);
spv = shortest_paths(v, adj);
vector<vector<ll>> DAGadj(n);
vector<ll> back(n);
for(ll i=0;i<n;i++){
if(sps[i] + spt[i] != sps[t])
continue;
for(pair<ll, ll> e:adj[i]){
if(sps[e.first] + spt[e.first] != sps[t])
continue;
if(sps[i] + e.second == sps[e.first]){
DAGadj[i].push_back(e.first);
back[e.first]++;
}
}
}
vector<array<ll, 4>> dp(n, {BIG, BIG, BIG, BIG});
vector<ll> topo;
stack<ll> q;
for(ll i=0;i<n;i++){
if(back[i] == 0)
q.push(i);
}
while(!q.empty()){
ll c = q.top();
q.pop();
topo.push_back(c);
for(ll e:DAGadj[c]){
back[e]--;
if(back[e] == 0)
q.push(e);
}
}
for(ll i:topo){
dp[i][0] = min(dp[i][0], spu[i]);
dp[i][1] = min(dp[i][1], spv[i]);
dp[i][2] = min(dp[i][2], spu[i]);
dp[i][3] = min(dp[i][3], spv[i]);
for(ll e:DAGadj[i]){
if(dp[i][0] <= dp[e][0]){
dp[e][0] = dp[i][0];
dp[e][1] = min(dp[i][1], spv[i]);
}
if(dp[i][3] <= dp[e][3]){
dp[e][2] = min(dp[i][2], spu[i]);
dp[e][3] = dp[i][3];
}
}
}
ll absmn = BIG;
for(ll i=0;i<n;i++){
absmn = min(absmn, min(dp[i][0] + dp[i][1], dp[i][2] + dp[i][3]));
}
cout << absmn << '\n';
}
