#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll INF = LLONG_MAX / 2;
constexpr int MAXN = 100001;
struct Edge {
int to;
ll cost;
};
vector<Edge> graph[MAXN];
ll distFromU[MAXN], distFromV[MAXN], distFromS[MAXN];
ll minUOnPath[MAXN], minVOnPath[MAXN];
bool visited[MAXN];
ll answer;
void dijkstra(int start, ll dist[]) {
fill(dist, dist + MAXN, INF);
fill(visited, visited + MAXN, false);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> pq;
pq.emplace(0, start);
dist[start] = 0;
while (!pq.empty()) {
auto [cost, node] = pq.top(); pq.pop();
if (visited[node]) continue;
visited[node] = true;
for (const Edge& e : graph[node]) {
if (dist[e.to] > dist[node] + e.cost) {
dist[e.to] = dist[node] + e.cost;
pq.emplace(dist[e.to], e.to);
}
}
}
}
void evaluatePath(int source, int target) {
fill(distFromS, distFromS + MAXN, INF);
fill(minUOnPath, minUOnPath + MAXN, INF);
fill(minVOnPath, minVOnPath + MAXN, INF);
fill(visited, visited + MAXN, false);
priority_queue<tuple<ll, int, int>, vector<tuple<ll, int, int>>, greater<>> pq;
pq.emplace(0, source, -1); // (cost, node, parent)
distFromS[source] = 0;
while (!pq.empty()) {
auto [cost, node, parent] = pq.top(); pq.pop();
if (visited[node]) continue;
visited[node] = true;
if (parent != -1) {
minUOnPath[node] = min(distFromU[node], minUOnPath[parent]);
minVOnPath[node] = min(distFromV[node], minVOnPath[parent]);
} else {
minUOnPath[node] = distFromU[node];
minVOnPath[node] = distFromV[node];
}
for (const Edge& e : graph[node]) {
if (distFromS[e.to] > distFromS[node] + e.cost) {
distFromS[e.to] = distFromS[node] + e.cost;
pq.emplace(distFromS[e.to], e.to, node);
}
}
}
answer = min(answer, minUOnPath[target] + minVOnPath[target]);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, S, T, U, V;
cin >> n >> m >> S >> T >> U >> V;
for (int i = 0; i < m; ++i) {
int a, b;
ll c;
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
dijkstra(U, distFromU);
dijkstra(V, distFromV);
answer = distFromU[V]; // No free commuter pass
// Try both directions for the commuter pass
evaluatePath(S, T);
evaluatePath(T, S);
cout << answer << '\n';
}
