#include "bits/stdc++.h"
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
using i32 = int;
using u32 = unsigned;
using i16 = short;
using u16 = unsigned short;
using ld = long double;
using ii = pair<int, int>;
const i64 inf = 1e16L;
int n, m, s, t, u, v;
vector<ii> edge;
vector<vector<int>> g, dag;
vector<i64> ds, du, dv, dp;
vector<int> state;
i64 ans = inf;
auto dijkstra(int s) {
vector<bool> seen(n, false);
vector<i64> dist(n, inf);
priority_queue<pair<i64, int>> pq;
dist[s] = 0;
pq.emplace(0LL, s);
while(!pq.empty()) {
auto [cst, v] = pq.top();
pq.pop();
if(seen[v]) continue;
cst *= -1;
seen[v] = true;
for(int id : g[v]) {
auto [u, w] = edge[id];
if(dist[u] <= cst + w) continue;
dist[u] = cst + w;
pq.emplace(-dist[u], u);
}
}
return dist;
}
vector<int> topo;
void dfs(int u) {
state[u] = 0;
if(u != t) {
for(int id : dag[u]) {
auto [v, w] = edge[id];
if(state[v] == -1) dfs(v);
if(state[v] == 1) {
dp[u] = min(dp[u], dp[v]);
state[u] = 1;
}
}
}
if(u == t) state[u] = 1;
if(state[u] == 1) {
dp[u] = min(dp[u], dv[u]);
ans = min(ans, du[u] + dp[u]);
topo.push_back(u);
}
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
--s, --t, --u, --v;
edge.resize(2 * m);
g.resize(n);
dag.resize(n);
state.assign(n, -1);
dp.assign(n, inf);
for(int i = 0; i < m; ++i) {
int a, b, c;
cin >> a >> b >> c;
--a, --b;
edge[2 * i] = {b, c};
edge[2 * i + 1] = {a, c};
g[a].push_back(2 * i);
g[b].push_back(2 * i + 1);
}
ds = dijkstra(s);
du = dijkstra(u);
dv = dijkstra(v);
for(int u = 0; u < n; ++u) {
for(int id : g[u]) {
auto [v, w] = edge[id];
if(ds[v] == ds[u] + w) dag[u].push_back(id);
}
}
dfs(s);
ans = min(ans, du[v]);
fill(dp.begin(), dp.end(), inf);
reverse(topo.begin(), topo.end());
for(int v : topo) {
dp[v] = dv[v];
for(int id : g[v]) {
auto [u, w] = edge[id];
ans = min(ans, du[v] + dp[u]);
dp[v] = min(dp[v], dp[u]);
}
}
cout << ans << '\n';
}
int main() {
ios_base :: sync_with_stdio(false);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) solve();
return 0;
}
