#include <bits/stdc++.h>
using namespace std;
#ifdef evenvalue
#include "debug.h"
#else
#define debug(...)
#endif
using int64 = long long;
using ld = long double;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
namespace Read {
int Int() {
int x;
cin >> x;
return x;
}
int64 Int64() {
int64 x;
cin >> x;
return x;
}
char Char() {
char c;
cin >> c;
return c;
}
string String() {
string s;
cin >> s;
return s;
}
double Double() {
return stod(String());
}
ld LongDouble() {
return stold(String());
}
template<typename T1, typename T2>
pair<T1, T2> Pair() {
pair<T1, T2> p;
cin >> p.first >> p.second;
return p;
}
template<typename T>
vector<T> Vec(const int n) {
vector<T> v(n);
for (T &x : v) {
cin >> x;
}
return v;
}
template<typename T>
vector<vector<T>> VecVec(const int n, const int m) {
vector<vector<T>> v(n);
for (vector<T> &vec : v) {
vec = Vec<T>(m);
}
return v;
}
}//namespace Read
constexpr int kInf = 1e9 + 10;
constexpr int64 kInf64 = 1e16 + 10;
constexpr int kMod = 1e9 + 7;
constexpr int kMaxN = 2e5 + 10;
auto dijkstra(const vector<vector<pair<int, int64>>> &g, const vector<int> &s) {
const int n = (int) g.size();
vector<int64> d(n, kInf64);
vector<vector<int>> p(n);
min_heap<pair<int64, int>> q;
for (const int x : s) {
d[x] = 0;
q.emplace(0, x);
}
while (not q.empty()) {
const auto [dist, x] = q.top();
q.pop();
if (d[x] < dist) continue;
for (const auto &[y, w] : g[x]) {
if (d[y] > d[x] + w) {
d[y] = d[x] + w;
p[y].clear();
q.emplace(d[y], y);
}
if (d[y] == d[x] + w) {
p[y].push_back(x);
}
}
}
return make_pair(d, p);
}
inline void solution() {
const auto n = Read::Int();
const auto m = Read::Int();
const auto s = Read::Int() - 1;
const auto t = Read::Int() - 1;
const auto u = Read::Int() - 1;
const auto v = Read::Int() - 1;
vector<vector<pair<int, int64>>> g(n);
for (int i = 0; i < m; i++) {
const auto x = Read::Int() - 1;
const auto y = Read::Int() - 1;
const auto w = Read::Int();
g[x].emplace_back(y, w);
g[y].emplace_back(x, w);
}
const auto foo = dijkstra(g, {s});
const auto &ds = foo.first;
const auto &p = foo.second;
const auto dt = dijkstra(g, {t}).first;
const auto du = dijkstra(g, {u}).first;
const auto dv = dijkstra(g, {v}).first;
vector<vector<int>> dag(n);
for (int y = 0; y < n; y++) {
if (ds[y] + dt[y] != ds[t]) continue;
for (const int x : p[y]) {
if (ds[x] + dt[x] != ds[t]) continue;
dag[x].push_back(y);
}
}
auto topsort = [&]() {
vector<int> order;
vector<bool> visit(n);
function<void(int)> dfs = [&](const int x) {
visit[x] = true;
for (const int y : dag[x]) {
if (not visit[y]) dfs(y);
}
order.push_back(x);
};
for (int x = 0; x < n; x++) {
if (ds[x] + dt[x] != ds[t]) continue;
if (not visit[x]) dfs(x);
}
return order;
};
const auto order = topsort();
vector<int64> best_u = du;
vector<int64> best_v = dv;
int64 ans = du[v];
for (const int x : order) {
for (const int y : dag[x]) {
best_u[x] = min(best_u[x], best_u[y]);
best_v[x] = min(best_v[x], best_v[y]);
}
ans = min(ans, best_u[x] + dv[x]);
ans = min(ans, best_v[x] + du[x]);
}
cout << ans << '\n';
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//freopen(".in", "r", stdin);
//freopen(".out", "w", stdout);
cout << fixed << setprecision(10);
int testcases = 1;
//cin >> testcases;
while (testcases--) {
solution();
}
}
