#include <bits/stdc++.h>
#define ll long long
#define db double
#define imx INT_MAX
#define imn INT_MIN
#define lmx LLONG_MAX
#define lmn LLONG_MIN
#define ld long double
#define lid id * 2 + 1
#define rid id * 2 + 2
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>
#define ordered_llset tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
const ll mod = 1e9 + 7;
struct edge_t {
int to;
ll c;
};
struct pqelem_t {
int at;
ll c;
};
auto cmp = [](const pqelem_t& a, const pqelem_t& b){return a.c > b.c;};
priority_queue<pqelem_t, vector<pqelem_t>, decltype(cmp)> pq(cmp);
void dijkstra(vector<ll>& best, vector<vector<edge_t>>& adj, int src) {
best[src] = 0;
pq.push({src, 0});
while (not pq.empty()) {
pqelem_t cur = pq.top();
pq.pop();
if (cur.c > best[cur.at]) continue;
for (auto& e : adj[cur.at]) {
if (cur.c + e.c < best[e.to]) {
best[e.to] = cur.c + e.c;
pq.push({e.to, cur.c + e.c});
}
}
}
}
vector<ll> dodp(vector<vector<edge_t>>& adj, int src, int dst, vector<ll>& vbest) {
int n = adj.size();
vector<ll> best(n, lmx);
vector<vector<int>> cands(n);
best[src] = 0;
pq.push({src, 0});
while (not pq.empty()) {
pqelem_t cur = pq.top();
pq.pop();
if (cur.c > best[cur.at]) continue;
for (auto& e : adj[cur.at]) {
if (cur.c + e.c < best[e.to]) {
best[e.to] = cur.c + e.c;
cands[e.to].clear();
cands[e.to].push_back(cur.at);
pq.push({e.to, cur.c + e.c});
} else if (cur.c + e.c == best[e.to]) cands[e.to].push_back(cur.at);
}
}
vector<vector<int>> cands2(n);
fill(best.begin(), best.end(), lmx);
best[dst] = 0;
pq.push({dst, 0});
while (not pq.empty()) {
pqelem_t cur = pq.top();
pq.pop();
if (cur.c > best[cur.at]) continue;
for (auto& e : adj[cur.at]) {
if (cur.c + e.c < best[e.to]) {
best[e.to] = cur.c + e.c;
cands2[e.to].clear();
cands2[e.to].push_back(cur.at);
pq.push({e.to, cur.c + e.c});
} else if (cur.c + e.c == best[e.to]) cands2[e.to].push_back(cur.at);
}
}
int i;
for (i = 0; i < n; i++) {
for (int elem : cands2[i]) cands[elem].push_back(i);
}
vector<vector<int>> dag(n);
unordered_set<int> seen;
for (i = 0; i < n; i++) {
seen.clear();
for (int elem : cands[i]) {
if (seen.find(elem) != seen.end()) dag[i].push_back(elem);
seen.insert(elem);
}
}
vector<int> indeg(n);
for (i = 0; i < n; i++) {
for (int elem : dag[i]) indeg[elem]++;
}
vector<ll> dp(n, lmx >> 1);
queue<int> q;
q.push(dst);
while (not q.empty()) {
int cur = q.front();
q.pop();
dp[cur] = min(dp[cur], vbest[cur]);
for (int to : dag[cur]) {
indeg[to]--;
if (indeg[to] == 0) q.push(to);
dp[to] = min(dp[to], dp[cur]);
}
}
return dp;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, i, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--;
t--;
u--;
v--;
vector<vector<edge_t>> adj(n);
for (i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<ll> ubest(n, lmx), vbest(n, lmx), sbest(n, lmx);
dijkstra(ubest, adj, u);
dijkstra(vbest, adj, v);
vector<ll> res1 = dodp(adj, s, t, vbest), res2 = dodp(adj, t, s, vbest);
ll ans = ubest[v];
for (i = 0; i < n; i++) ans = min(ans, ubest[i] + min(res1[i], res2[i]));
cout << ans;
return 0;
}
