#include <bits/stdc++.h>
using namespace std;
long long inf = 1e17;
int n;
vector<vector<pair<int, long long>>> graph;
vector<long long> dijkstra(int s) {
vector<long long> dis(n, inf);
vector<int> vis(n);
dis[s] = 0;
priority_queue<pair<long long, int>> pq;
pq.push({0, s});
while (pq.size() > 0) {
auto t = pq.top();
pq.pop();
if (vis[t.second]) {
continue;
}
vis[t.second] = 1;
for (auto adj : graph[t.second]) {
if (adj.second + dis[t.second] < dis[adj.first]) {
dis[adj.first] = adj.second + dis[t.second];
pq.push({-dis[adj.first], adj.first});
}
}
}
return dis;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
graph.resize(n);
for (int i = 0; i < m; i++) {
int a, b; long long c;
cin >> a >> b >> c;
graph[--a].push_back({--b, c});
graph[b].push_back({a, c});
}
vector<long long> u_dis = dijkstra(u);
vector<long long> u_par = u_dis;
vector<long long> u_child = u_dis;
vector<long long> v_dis = dijkstra(v);
vector<long long> dis(n, inf);
vector<vector<int>> par(n);
vector<int> vis(n);
dis[s] = 0;
priority_queue<pair<long long, int>> pq;
pq.push({0, s});
while (pq.size() > 0) {
auto t = pq.top();
pq.pop();
if (vis[t.second]) {
continue;
}
vis[t.second] = 1;
for (auto adj : graph[t.second]) {
if (adj.second + dis[t.second] < dis[adj.first]) {
dis[adj.first] = adj.second + dis[t.second];
par[adj.first].clear();
par[adj.first].push_back(t.second);
pq.push({-dis[adj.first], adj.first});
} else if (adj.second + dis[t.second] == dis[adj.first]) {
par[adj.first].push_back(t.second);
}
}
}
vector<int> on(n);
queue<int> q;
on[t] = 1;
q.push(t);
while (q.size() > 0) {
int f = q.front();
q.pop();
for (auto adj : par[f]) {
if (!on[adj]) {
on[adj] = 1;
q.push(adj);
}
}
}
vector<vector<int>> child(n);
for (int i = 0; i < n; i++) {
if (on[i]) {
for (int j = 0; j < par[i].size(); j++) {
child[par[i][j]].push_back(i);
}
pq.push({-u_dis[i], i});
}
}
while (pq.size() > 0) {
auto t = pq.top();
pq.pop();
long long d = -t.first;
if (u_par[t.second] >= d) {
queue<int> q;
q.push(t.second);
while (q.size() > 0) {
for (auto adj : par[q.front()]) {
if (u_par[adj] > d && on[adj]) {
u_par[adj] = d;
q.push(adj);
}
}
q.pop();
}
}
if (u_child[t.second] >= d) {
queue<int> q;
q.push(t.second);
while (q.size() > 0) {
for (auto adj : child[q.front()]) {
if (u_child[adj] > d && on[adj]) {
u_child[adj] = d;
q.push(adj);
}
}
q.pop();
}
}
}
long long out = inf;
for (int i = 0; i < n; i++) {
long long m_u = min(u_child[i], u_par[i]);
out = min(out, m_u + v_dis[i]);
}
cout << out << "\n";
}
