#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template<class T> bool cmin(T &i, T j) { return i > j ? i=j,true:false; }
template<class T> bool cmax(T &i, T j) { return i < j ? i=j,true:false; }
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m;
cin >> n >> m;
int s,t,u,v;
cin >> s >> t >> u >> v;
--s,--t,--u,--v;
vector<vector<pair<int,int>>> adj(n);
for (int x,y,w;m--;) {
cin >> x >> y >> w;
--x,--y;
adj[x].emplace_back(y,w);
adj[y].emplace_back(x,w);
}
const ll inf = 1e18;
auto dijkstra = [&](int source) {
vector<ll> dist(n,inf);
dist[source] = 0;
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> q;
q.emplace(0,source);
while(!q.empty()) {
auto [d,x] = q.top(); q.pop();
if (dist[x] != d) { continue; }
for (auto &[y,w]: adj[x]) if (cmin(dist[y],dist[x]+w)) {
q.emplace(dist[y],y);
}
}
return dist;
};
vector<vector<int>> sp_adj(n);
auto D = dijkstra(s);
vector<bool> in_sp(n);
queue<int> q;
q.push(t);
in_sp[t] = true;
vector<int> in(n);
while(!q.empty()) {
int x = q.front(); q.pop();
for (auto &[y,w]: adj[x]) if (D[x] == D[y] + w) {
sp_adj[x].push_back(y);
// cout << "added reverse-edge " << 1+x << " " << 1+y << endl;
in[y]++;
if (!in_sp[y]) {
in_sp[y] = true;
q.push(y);
}
}
}
auto DU = dijkstra(u), DV = dijkstra(v);
vector<ll> dp(n,inf),dp2(n,inf);
assert(in[t] == 0);
q.push(t);
ll ans = DU[v];
while(!q.empty()) {
int x = q.front(); q.pop();
cmin(dp[x],DV[x]);
cmin(dp2[x],DU[x]);
cmin(ans,dp[x]+DU[x]);
cmin(ans,dp2[x]+DV[x]);
for (int &y: sp_adj[x]) {
cmin(dp[y],dp[x]);
cmin(dp2[y],dp2[x]);
if (--in[y] == 0) {
q.push(y);
}
}
}
cout << ans << endl;
}
