#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = numeric_limits<ll>::max() / 4;
vector<ll> dijkstra(int src, const vector<vector<pair<int,ll>>> &adj) {
int n = adj.size();
vector<ll> dist(n, INF);
using pli = pair<ll,int>;
priority_queue<pli, vector<pli>, greater<pli>> pq;
dist[src] = 0;
pq.emplace(0, src);
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d != dist[u]) continue;
for (auto &[v, w] : adj[u]) {
if (dist[v] > d + w) {
dist[v] = d + w;
pq.emplace(dist[v], v);
}
}
}
return dist;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, M;
cin >> N >> M;
int S, T; cin >> S >> T;
int U, V; cin >> U >> V;
vector<vector<pair<int,ll>>> adj(N + 1);
vector<tuple<int,int,ll>> edges;
edges.reserve(M);
for (int i = 0; i < M; ++i) {
int a, b; ll c;
cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
edges.emplace_back(a, b, c);
}
auto dS = dijkstra(S, adj);
auto dT = dijkstra(T, adj);
auto dU = dijkstra(U, adj);
auto dV = dijkstra(V, adj);
ll bestST = dS[T];
// Build shortest-path DAG
vector<vector<int>> dag(N + 1);
for (auto &[a, b, c] : edges) {
if (dS[a] + c + dT[b] == bestST) dag[a].push_back(b);
if (dS[b] + c + dT[a] == bestST) dag[b].push_back(a);
}
// Mark nodes on some SP from S to T
vector<char> fromS(N + 1, 0), toT(N + 1, 0);
{ // BFS from S
queue<int> q;
q.push(S); fromS[S] = 1;
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : dag[u]) if (!fromS[v]) {
fromS[v] = 1;
q.push(v);
}
}
}
{ // reverse-DAG BFS from T
vector<vector<int>> dag_rev(N + 1);
for (int u = 1; u <= N; ++u)
for (int v : dag[u]) dag_rev[v].push_back(u);
queue<int> q;
q.push(T); toT[T] = 1;
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : dag_rev[u]) if (!toT[v]) {
toT[v] = 1;
q.push(v);
}
}
}
// DFS to enumerate SP nodes in DAG (pruned to nodes reaching T)
vector<int> ord(N + 1, 0), rev; rev.reserve(N + 1);
vector<int> parent; parent.reserve(N + 1);
int K = 0;
function<void(int)> dfs = [&](int u) {
ord[u] = ++K;
rev.push_back(u);
for (int v : dag[u]) {
if (fromS[v] && toT[v] && !ord[v]) {
dfs(v);
parent.push_back(ord[u]);
}
}
};
dfs(S);
// rev[i] is 0-indexed list of original nodes in DFS order; ord maps original to 1-based index
// parent list is built in same order as rev except first element (S) has no parent
vector<int> par(K+1);
par[1] = 0;
for (int i = 2; i <= K; ++i) par[i] = parent[i-2];
// Build reduced graph for dominator computation
vector<vector<int>> g(K+1), rg(K+1);
for (int idx = 0; idx < K; ++idx) {
int u = rev[idx];
for (int v : dag[u]) {
if (fromS[v] && toT[v]) {
int iu = ord[u], iv = ord[v];
g[iu].push_back(iv);
rg[iv].push_back(iu);
}
}
}
// Lengauer-Tarjan dominator tree
vector<int> sdom(K+1), dom(K+1), dsu(K+1), label(K+1);
vector<vector<int>> bucket(K+1);
for (int i = 1; i <= K; ++i) {
sdom[i] = label[i] = dsu[i] = i;
dom[i] = 0;
}
function<int(int)> find = [&](int u) {
if (dsu[u] == u) return u;
int v = find(dsu[u]);
if (sdom[label[dsu[u]]] < sdom[label[u]]) label[u] = label[dsu[u]];
return dsu[u] = v;
};
auto unite = [&](int u, int v){ dsu[v] = u; };
for (int i = K; i >= 2; --i) {
for (int j : rg[i]) {
find(j);
sdom[i] = min(sdom[i], sdom[label[j]]);
}
bucket[sdom[i]].push_back(i);
unite(par[i], i);
for (int j : bucket[par[i]]) {
find(j);
dom[j] = (sdom[label[j]] < sdom[j]) ? label[j] : par[i];
}
bucket[par[i]].clear();
}
for (int i = 2; i <= K; ++i) {
if (dom[i] != sdom[i]) dom[i] = dom[dom[i]];
}
dom[1] = 0;
// Build dominator tree children
vector<vector<int>> tree(K+1);
for (int i = 2; i <= K; ++i) tree[dom[i]].push_back(i);
// Compute Bmin over dominator subtree: Bmin_tree[i] = min dV over rev-subtree
vector<ll> Bmin_tree(K+1, INF);
for (int i = 1; i <= K; ++i) {
int u = rev[i-1];
Bmin_tree[i] = dV[u];
}
function<void(int)> dfs_bmin = [&](int u) {
for (int v : tree[u]) {
dfs_bmin(v);
Bmin_tree[u] = min(Bmin_tree[u], Bmin_tree[v]);
}
};
dfs_bmin(1);
// Compute answer
ll answer = dU[V];
for (int i = 1; i <= K; ++i) {
int u = rev[i-1];
if (dU[u] < INF && Bmin_tree[i] < INF) {
answer = min(answer, dU[u] + Bmin_tree[i]);
}
}
cout << answer << '\n';
return 0;
}
