#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <array>
#include <stack>
#include <queue>
#include <random>
#include <numeric>
#include <functional>
#include <chrono>
#include <utility>
#include <iomanip>
#include <assert.h>
using namespace std;
void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#define rng_init mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define rng_seed(x) mt19937 rng(x)
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define int long long
template<typename T>
struct Dijkstra {
const T INF = numeric_limits<T>::max();
struct state {
int u;
T dist;
state() {}
state(int _u, T _dist) : u(_u), dist(_dist) {}
bool operator<(const state &other) const {
return dist > other.dist;
}
};
int n;
vector<vector<pair<int, T>>> graph;
vector<T> dist;
vector<int> parent;
Dijkstra(int _n = 0) {
init(_n);
}
void init(int _n) {
n = _n;
graph.resize(n);
}
void add_directional_edge(int u, int v, T weight) {
graph[u].emplace_back(v, weight);
}
void add_bidirectional_edge(int u, int v, T weight) {
add_directional_edge(u, v, weight);
add_directional_edge(v, u, weight);
}
void run(const vector<int> &source) {
priority_queue<state> pq;
dist.assign(n, INF);
parent.assign(n, -1);
for (const auto &u : source) {
dist[u] = 0;
parent[u] = u;
pq.emplace(u, 0);
}
while (!pq.empty()) {
auto [u, cur_dist] = pq.top();
pq.pop();
if (dist[u] != cur_dist) continue;
for (const auto &[v, weight] : graph[u]) {
T new_dist = cur_dist + weight;
if (new_dist < dist[v]) {
dist[v] = new_dist;
parent[v] = u;
pq.emplace(v, new_dist);
}
}
}
}
bool reachable(int u) {
return dist[u] < INF;
}
};
const int MXN = 1e5 + 5, INF = 1e18;
void solve() {
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
Dijkstra<int> solver(N + 1);
while (M--) {
int u, v, wt;
cin >> u >> v >> wt;
solver.add_bidirectional_edge(u, v, wt);
}
solver.run(vector<int>{U});
vector<int> u_dist = solver.dist;
int ans = u_dist[V];
solver.run(vector<int>{V});
vector<int> v_dist = solver.dist;
solver.run(vector<int>{S});
vector<int> s_dist = solver.dist;
solver.run(vector<int>{T});
vector<int> t_dist = solver.dist;
vector<pair<int, int>> dag_order;
for (int i = 1; i < sz(s_dist); i++)
dag_order.emplace_back(s_dist[i], i);
sort(all(dag_order));
vector<int> dp1(N + 1, INF), dp2(N + 1, INF);
for (const auto &[cur_dist, node] : dag_order) {
dp1[node] = u_dist[node];
dp2[node] = v_dist[node];
for (const auto &[v, wt] : solver.graph[node]) {
if (s_dist[v] > s_dist[node]) continue;
if (s_dist[v] + wt + t_dist[node] == s_dist[T]) {
ans = min({ans, dp1[v] + v_dist[node], dp2[v] + u_dist[node]});
dp1[node] = min(dp1[node], dp1[v]);
dp2[node] = min(dp2[node], dp2[v]);
}
}
}
cout << ans;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int TC = 1;
// cin >> TC;
while (TC--) solve();
}
