#include <bits/stdc++.h>
#ifdef DEBUG
#include "debug.hpp"
#endif
using namespace std;
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define traverse(c, it) for(auto it = (c).begin(); it != (c).end(); ++it)
#define rep(i, N) for(int i = 0; i < (N); ++i)
#define rrep(i, N) for(int i = (N) - 1; i >= 0; --i)
#define rep1(i, N) for(int i = 1; i <= (N); ++i)
#define rep2(i, s, e) for(int i = (s); i <= (e); ++i)
#ifdef DEBUG
#define debug(x...) { \
++dbg::depth; \
string dbg_vals = dbg::to_string(x); \
--dbg::depth; \
dbg::fprint(__func__, __LINE__, #x, dbg_vals); \
}
#define light_debug(x) { \
dbg::light = true; \
dbg::dout << __func__ << ":" << __LINE__; \
dbg::dout << " " << #x << " = " << x << endl; \
dbg::light = false; \
}
#else
#define debug(x...) 42
#define light_debug(x) 42
#endif
using ll = long long;
template<typename T>
inline T& ckmin(T& a, T b) { return a = a > b ? b : a; }
template<typename T>
inline T& ckmax(T& a, T b) { return a = a < b ? b : a; }
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int N, M, S, T, U, V; cin >> N >> M >> S >> T >> U >> V; --S, --T, --U, --V;
vector<vector<pair<int, long long>>> adj(N);
rep(i, M) {
int u, v; long long w; cin >> u >> v >> w; --u, --v;
adj[u].push_back({v, w}), adj[v].push_back({u, w});
}
auto dijkstra = [&](int s) -> vector<long long> {
vector<long long> dist(N, -1);
priority_queue<pair<long long, int>,
vector<pair<long long, int>>,
greater<pair<long long, int>>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if(~dist[u]) continue;
dist[u] = d;
for(auto [v, w]: adj[u])
if(dist[v] == -1)
pq.push({d + w, v});
}
return dist;
};
vector<long long> dist_u = dijkstra(U), dist_v = dijkstra(V);
auto dijkstra2 = [&]() -> long long {
struct dist_t {
long long d_s, d_u, d_v;
bool operator >(const dist_t& d) const {
return d_s > d.d_s || (d_s == d.d_s && d_u + d_v > d.d_u + d.d_v);
}
};
auto add_edge = [&](dist_t d, int u, int v, long long w) -> dist_t {
long long m_u = min({dist_u[u], dist_u[v], d.d_u});
long long m_v = min({dist_v[u], dist_v[v], d.d_v});
return {d.d_s += w, m_u, m_v};
};
auto comp = [](const pair<dist_t, int>& a, const pair<dist_t, int>& b) {
if(a.first > b.first)
return true;
if(b.first > a.first)
return false;
return a.second > b.second;
};
vector<dist_t> dist(N);
vector<bool> vis(N);
priority_queue<pair<dist_t, int>,
vector<pair<dist_t, int>>,
decltype(comp)> pq(comp);
pq.push({dist_t{0, dist_u[S], dist_v[S]}, S});
while(!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if(vis[u]) continue;
vis[u] = true;
dist[u] = d;
for(auto [v, w]: adj[u])
if(!vis[v])
pq.push({add_edge(d, u, v, w), v});
}
return dist[T].d_u + dist[T].d_v;
};
cout << min(dijkstra2(), dist_u[V]) << '\n';
#ifdef DEBUG
dbg::dout << "\nExecution time: "
<< clock() * 1000 / CLOCKS_PER_SEC
<< "ms" << endl;
#endif
return 0;
}
