#include <bits/stdc++.h>
using namespace std;
using ll = long long;
// using ld = long double;
#define all(x) begin(x), end(x)
#ifdef LOCAL
#define debug(...) __VA_ARGS__;
#else
#define debug(...)
#endif
template<class A, class B> ostream& operator<<(ostream& os, const pair<A, B> &p);
template<class T> ostream& operator<<(ostream& os, const vector<T> &v);
template<class T, size_t N> ostream& operator<<(ostream& os, const array<T, N> &v);
template<class A, class B>
ostream& operator<<(ostream& os, const pair<A, B> &p) {
return os << '(' << p.first << ',' << p.second << ')';
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &v) {
os << '{'; bool fs = 1;
for(auto &i : v) { if(!fs) os << ','; os << i; fs = 0; }
return os << '}';
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &v) {
os << '{'; bool fs = 1;
for(auto &i : v) { if(!fs) os << ','; os << i; fs = 0; }
return os << '}';
}
void init() {
}
void solve(int tt = 0) {
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int s2, t2; cin >> s2 >> t2;
struct Edge {
int u, v, w;
Edge() {}
Edge(int u, int v, int w) : u(u), v(v), w(w) {}
inline int get_other(int x) {
return x == u ? v : u;
};
};
vector<Edge> edges;
vector adj(n+1, vector<int>());
for(int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back(edges.size());
adj[v].emplace_back(edges.size());
edges.push_back(Edge(u, v, w));
}
const ll INF = 1e18;
const auto dijkstra = [&](int s, int t) {
vector<ll> dist(n+1, INF);
vector<int> vis(n+1, 0);
vector<vector<pair<int, int>>> par(n+1);
using state = pair<ll, int>;
priority_queue<state, vector<state>, greater<state>> pq;
pq.push({dist[s] = 0, s});
while(!pq.empty()) {
int u = pq.top().second; pq.pop();
if(u == t) break;
if(vis[u]) continue;
vis[u] = 1;
for(int i : adj[u]) {
int v = edges[i].get_other(u);
int w = edges[i].w;
if(vis[v]) continue;
if(dist[v] > dist[u] + w) {
par[v].clear();
par[v].emplace_back(u, i);
pq.push({dist[v] = dist[u] + w, v});
} else if(dist[v] == dist[u] + w) {
par[v].emplace_back(u, i);
}
}
}
return make_pair(dist[t], par);
};
vector par = dijkstra(s, t).second;
vector<vector<pair<int, int>>> go(n+1);
vector<int> ind;
{
vector<int> vis(n+1, 0);
const auto dfs = [&](const auto &dfs, int u) -> void {
vis[u] = 1;
ind.push_back(u);
for(auto &[v, _] : par[u]) if(!vis[v]) {
dfs(dfs, v);
}
};
dfs(dfs, t);
}
for(int i : ind) go[i] = par[i];
vector<vector<pair<int, int>>> rev(n+1);
for(int u = 1; u <= n; u++) {
for(auto &[v, i] : go[u]) {
rev[v].emplace_back(u, i);
}
}
debug(cerr << "ind = " << ind << '\n');
debug({
cerr << "go = " << '\n';
for(int i = 1; i <= n; i++)
cerr << "i = " << i << " : " << go[i] << '\n';
});
debug({
cerr << "rev = " << '\n';
for(int i = 1; i <= n; i++)
cerr << "i = " << i << " : " << rev[i] << '\n';
});
const auto dijkstra2 = [&](int s, int t) {
// dist[u][stat{0,1,2,3}]
vector dist(n+1, vector<ll>(4, INF));
vector vis(n+1, vector<int>(4, 0));
using state = tuple<ll, int, int>;
priority_queue<state, vector<state>, greater<state>> pq;
pq.push({dist[s][0] = 0, s, 0});
while(!pq.empty()) {
auto [d, u, stat] = pq.top(); pq.pop();
if(vis[u][stat]) continue;
debug(cerr << u << ' ' << stat << " -> " << d << '\n');
vis[u][stat] = 1;
if(stat == 0 || stat == 3) {
for(int i : adj[u]) {
int v = edges[i].get_other(u);
int w = edges[i].w;
if(vis[v][stat]) continue;
if(dist[v][stat] > d + w) {
pq.push({dist[v][stat] = d + w, v, stat});
}
}
if(stat == 0 && !go[u].empty() && dist[u][1] > d) {
pq.push({dist[u][1] = d, u, 1});
}
if(stat == 0 && !rev[u].empty() && dist[u][2] > d) {
pq.push({dist[u][2] = d, u, 2});
}
} else if(stat == 1) { // normal
for(auto [v, _] : go[u]) {
if(vis[v][stat]) continue;
if(dist[v][stat] > d) {
pq.push({dist[v][stat] = d, v, stat});
}
}
if(dist[u][3] > d) {
pq.push({dist[u][3] = d, u, 3});
}
} else { // rev
for(auto [v, _] : rev[u]) {
if(vis[v][stat]) continue;
if(dist[v][stat] > d) {
pq.push({dist[v][stat] = d, v, stat});
}
}
if(dist[u][3] > d) {
pq.push({dist[u][3] = d, u, 3});
}
}
}
debug(cerr << dist[t] << '\n');
return *min_element(dist[t].begin(), dist[t].end());
};
cout << dijkstra2(s2, t2) << '\n';
}
void reset() {
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
int t = 1; // cin >> t;
init();
for(int i = 1; i <= t; i++) solve(i), reset();
return 0;
}
