#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
vector<pair<ll,ll>> adj[100001];
ll n, m;
vector<ll> dijkstra(ll start){
vector<ll> dist(n+1, LLONG_MAX);
// Dijkstra's algorithm
using T = pair<long long, ll>;
priority_queue<T, vector<T>, greater<T>> pq;
dist[start] = 0; // The shortest path from a node to itself is 0
pq.push({0, start});
while (!pq.empty()) {
const auto [cdist, node] = pq.top();
pq.pop();
if (cdist != dist[node]) { continue; }
for (const pair<ll, ll> &i : adj[node]) {
// If we can reach a neighbouring node faster,
// we update its minimum distance
if (cdist + i.first < dist[i.second]) {
pq.push({dist[i.second] = cdist + i.first, i.second});
}
}
}
return dist;
}
ll solve(ll a, ll b, ll c, ll d){
vector<ll> path1 = dijkstra(a),path2 = dijkstra(b),sus1=dijkstra(c),sus2=dijkstra(d);
vector<ll> dp(n+1,LLONG_MAX/4),dp1(n+1,LLONG_MAX/4),dp2(n+1,LLONG_MAX/4);
// vector<pair<ll,ll>> dp1(n+1,{LLONG_MAX,LLONG_MAX}),dp2(n+1,{LLONG_MAX,LLONG_MAX});
vector<pair<ll,ll>> elza;
for(ll i=1;i<=n;i++){
if(path1[i]+path2[i]==path1[b])elza.push_back({path1[i],i});
}
dp[a]=sus1[a]+sus2[a];
dp1[a]=sus1[a];
dp2[a]=sus2[a];
sort(elza.begin(),elza.end());
for(ll i=0;i<elza.size();i++){
ll v = elza[i].second;
for(auto [cost, w] : adj[v]){
if(path1[v]+path2[v]==path1[b]&&path1[w]<path1[v]){
dp1[v]=min(dp1[w],sus1[v]);
dp2[v]=min(dp2[w],sus2[v]);
dp[v]=min(dp[v],dp[w]);
}
}
for(auto [cost, w] : adj[v]){
if(path1[v]+path2[v]==path1[b]&&path1[w]<path1[v]){
dp[v]=min(dp[v],dp1[v]+sus2[v]);
dp[v]=min(dp[v],dp2[v]+sus1[v]);
}
}
// cout << v <<' ' << path1[v] << ": " << dp[v] << ' ' << dp1[v] << ' ' << dp2[v] << '\n';
}
return min(dp[b],sus1[d]);
}
int main(){
cin.tie(0)->sync_with_stdio(0);
ll a,b,c,d;
cin >> n >> m >> a >> b >> c >> d;
for(ll i=0;i<m;i++){
ll x,y,cost; cin >> x >> y >> cost;
adj[x].push_back({cost,y});
adj[y].push_back({cost,x});
}
cout << min(solve(a,b,c,d),solve(b,a,c,d));
// cout << '\n';
// for(ll i = 0;i<elza.size();i++)cout << elza[i].first << ' ' << elza[i].second << '\n';
// cout << '\n';
return 0;
}
