#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define pb push_back
#define all(a) a.begin(), a.end()
#define endl "\n"
void printVector(vector<int> a){
for (auto x: a) cout << x << " ";
cout << endl;
}
vector<vector<pair<int, int>>> graph;
vector<int> distu;
vector<int> distv;
vector<int> dp1;
vector<int> dp2;
void dijkstra(int s, int n, vector<int> &arr){
arr[s] = 0;
priority_queue<pair<int, int>> pq;
pq.push({0, s});
vector<int> visited(n+1);
while (!pq.empty()){
int c, node;
tie(c, node) = pq.top();
pq.pop();
if (!visited[node]){
arr[node] = -c;
visited[node] = 1;
for (auto x: graph[node]) pq.push({c-x.second, x.first});
}
}
}
int ans = 1e17;
void dijkstra2(int s, int e, int n){
vector<int> visited(n+1);
vector<int> ds(n+1, 1e17);
dp1.resize(n+1, 1e17);
dp2.resize(n+1, 1e17);
priority_queue<pair<int, pair<int, int>>> pq;
pq.push({0, {s, 0}});
while (!pq.empty()){
int c, node, par;
pair<int, int> p;
tie(c, p) = pq.top();
pq.pop();
tie(node, par) = p;
if (!visited[node]){
visited[node] = 1;
ds[node] = -c;
dp1[node] = min(distu[node], dp1[par]);
dp2[node] = min(distv[node], dp2[par]);
for (auto x: graph[node]) pq.push({c-x.second, {x.first, node}});
}else if (-c == ds[node]){
if (min(distu[node], dp1[par])+min(distv[node], dp2[par]) <=
dp1[node]+dp2[node]){
dp1[node] = min(distu[node], dp1[par]);
dp2[node] = min(distv[node], dp2[par]);
}
}
}
ans = min(ans, dp1[e]+dp2[e]);
}
void solve(){
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
graph.resize(n+1);
distu.resize(n+1, 1e17);
distv.resize(n+1, 1e17);
dp1.resize(n+1, 1e17);
dp2.resize(n+1, 1e17);
FOR(i,0,m){
int a, b, c; cin >> a >> b >> c;
graph[a].pb({b, c});
graph[b].pb({a, c});
}
dijkstra(u, n, distu);
dijkstra(v, n, distv);
ans = distu[v];
dijkstra2(s, t, n);
dp1.clear();
dp2.clear();
dijkstra2(t, s, n);
cout << ans << endl;
}
int32_t main(){
ios::sync_with_stdio(false);cin.tie(nullptr);
int t = 1; // cin >> t;
while (t--) solve();
}
