#include <bits/stdc++.h>
#define int ll
#define FOR(i,k,n) for(int i = k; i <= n; i++)
#define FORR(i,k,n) for(int i = n; i >= k; i--)
#define pb push_back
#define all(x) begin(x),end(x)
#define fi first
#define se second
#define BIT(S, i) (((S)>>(i))&1)
#define MASK(i) ((1ll)<<(i))
#define name "loopy"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef long double ld;
template<class X, class Y>
bool maximize(X &a, Y b) {
if (a < b) {a = b; return true;}
return false;
}
template<class X, class Y>
bool minimize(X &a, Y b) {
if (a > b) {a = b; return true;}
return false;
}
const int N = 1e5+6;
const int INF = 1e18;
int m, n, s, t, u, v, ans;
vector<pii> adj[N];
vi dist1, dist2, dp1, dp2, d;
void dijkstra(vi &di, int s) {
di.assign(N, INF);
di[s] = 0;
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, s});
while (q.size()) {
auto [du, u] = q.top(); q.pop();
if (du != di[u]) continue;
for (auto [v, w] : adj[u]) {
if (di[v] > di[u] + w) {
di[v] = di[u] + w;
q.push({di[v], v});
}
}
}
}
int dijkstra2(int s, int t) {
d.assign(N, INF);
dp1.assign(N, INF);
dp2.assign(N, INF);
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, s});
d[s] = 0;
dp1[s] = dist1[s]; dp2[s] = dist2[s];
while (q.size()) {
auto [du, u] = q.top(); q.pop();
if (du != d[u]) continue;
for (auto [v, w] : adj[u]) {
if (d[v] > d[u] + w) {
d[v] = d[u] + w;
q.push({d[v], v});
dp1[v] = min(dist1[v], dp1[u]);
dp2[v] = min(dist2[v], dp2[u]);
} else if (d[v] == d[u] + w) {
int minV = min(dp2[u], dist2[v]);
int minU = min(dp1[u], dist1[v]);
if (minU + minV <= dp1[v] + dp2[v]) {
dp1[v] = minU;
dp2[v] = minV;
}
}
}
}
return dp1[t] + dp2[t];
}
void solve() {
FOR(i,0,N-1) adj[i].clear();
cin >> n >> m >> s >> t >> u >> v;
while (m--) {
int x, y, z; cin >> x >> y >> z;
adj[x].pb({y, z});
adj[y].pb({x, z});
}
dijkstra(dist1, u);
dijkstra(dist2, v);
ans = dist1[v];
minimize(ans, dijkstra2(s,t));
minimize(ans, dijkstra2(t,s));
cout << ans << '\n';
}
main(){
ios_base::sync_with_stdio(0); cin.tie(0);
if (fopen(name".inp","r")) {
freopen(name".inp","r",stdin);
freopen(name".out","w",stdout);
}
solve();
}
