#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define all(x) x.begin(), x.end()
template <typename T1, typename T2> inline void chkmin(T1 &x, const T2 & y) {if (x > y) x = y;}
template <typename T1, typename T2> inline void chkmax(T1 &x, const T2 & y) {if (x < y) x = y;}
#define int ll
struct edge{
int to, cost;
edge() {}
edge(int _to, int _cost) {
to = _to, cost = _cost;
}
};
const int MAXN = 1e5 + 10;
vector<edge> g[MAXN];
int n, m;
int s1, t1;
int s2, t2;
void read() {
cin >> n >> m;
cin >> s1 >> t1;
s1--;
t1--;
cin >> s2 >> t2;
s2--;
t2--;
for (int i = 0; i < m; i++) {
int u, v;
int c;
cin >> u >> v >> c;
u--;
v--;
g[u].push_back({v, c});
g[v].push_back({u, c});
}
}
const ll INF = 1e18;
ll ans;
vector<ll> djkstra(int v) {
vector<ll> d(n, INF);
set<pair<ll, int>> q;
d[v] = 0;
q.insert({0, v});
while (!q.empty()) {
int v = q.begin()->second;
q.erase(q.begin());
for (auto [to, cost] : g[v]) {
if (d[to] <= d[v] + cost) continue;
q.erase({d[to], to});
d[to] = d[v] + cost;
q.insert({d[to], to});
}
}
return d;
}
vector<ll> dist;
void build() {
auto d = djkstra(s1);
dist.assign(n, INF);
queue<int> q;
q.push(t1);
dist[t1] = d[t1];
while (!q.empty()) {
int v = q.front();
q.pop();
for (auto [to, cost] : g[v]) {
if (dist[to] != INF) continue;
if (d[to] + cost != d[v]) continue;
dist[to] = d[to];
q.push(to);
}
}
}
vector<ll> dp1;
vector<bool> used;
ll dfs1(int v) {
if (used[v]) return dp1[v];
used[v] = true;
for (auto [to, cost] : g[v]) {
if (dist[v] + cost != dist[to]) continue;
chkmin(dp1[v], dfs1(to));
}
return dp1[v];
}
vector<ll> dp2;
ll dfs2(int v) {
if (used[v]) return dp2[v];
used[v] = true;
for (auto [to, cost] : g[v]) {
if (dist[v] != dist[to] + cost) continue;
chkmin(dp2[v], dfs2(to));
}
return dp2[v];
}
void run() {
build();
dp1 = dp2 = djkstra(t2);
used.assign(n, false);
dfs1(s1);
used.assign(n, false);
dfs2(t1);
vector<ll> have = djkstra(s2);
ans = have[t2];
for (int i = 0; i < n; i++) {
if (dist[i] == INF) continue;
chkmin(ans, min(dp1[i], dp2[i]) + have[i]);
}
}
void write() {
cout << ans << endl;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
read();
run();
write();
return 0;
}
