#include <cstdio>
#include <vector>
#include <algorithm>
#include <queue>
#include <utility>
using namespace std;
#define MAXNUM 1000000000
#define MAXN 100000
#define MAXM 200000
#define INF ((long long) (1e18))
struct edge {
int x, y, len;
};
vector<long long> Dinit, Dtrans;
vector<vector<pair<int, int> > > G;
vector <edge> E;
void Dijkstra(int s, int N, vector<long long> &dist) {
priority_queue<pair<long long, int> > PQ;
for (int i = 0; i < N; i++) dist[i] = INF;
dist[s] = 0;
PQ.push(make_pair(-dist[s], s));
while (!PQ.empty()) {
pair<long long, int> front = PQ.top();
PQ.pop();
long long w = -front.first, u = front.second;
if (w > dist[u] || w == INF) continue;
for (int p = 0; p < G[u].size(); p++) {
pair<int, int> v = G[u][p];
long long tmp = min(dist[v.first], dist[u] + v.second);
if (dist[v.first] > tmp) {
dist[v.first] = tmp;
PQ.push(make_pair(-tmp, v.first));
}
}
}
}
void solve_large(int N, int M, int t, int a, int b) {
for (int i = 0; i < N; i++) G[i].resize(0);
for (int i = 0; i < M; i++) {
int u = E[i].x, v = E[i].y, d = E[i].len;
if (Dinit[u] + Dtrans[v] + d == Dinit[t]) {
G[u].push_back(make_pair(v, 0)); // direction u -> v, no cost
G[v].push_back(make_pair(u, d)); // direction v -> u, full cost
}
else if (Dinit[v] + Dtrans[u] + d == Dinit[t]) {
G[v].push_back(make_pair(u, 0)); // direction v -> u, no cost
G[u].push_back(make_pair(v, d)); // direction u -> v, full cost
}
else {
G[v].push_back(make_pair(u, d)); // direction v -> u, full cost
G[u].push_back(make_pair(v, d)); // direction u -> v, full cost
}
}
Dijkstra(a, N, Dinit);
Dijkstra(b, N, Dtrans);
printf("%lld\n", min(Dinit[b], Dtrans[a]));
}
int main() {
int N, M, s, t, a, b;
scanf("%d%d", &N, &M);
if (N < 1 || N > MAXN || M < 1 || M > MAXM) {
fprintf(stderr, "Error in input (N = %d, M = %d)\n", N, M);
return 1;
}
scanf("%d%d", &s, &t); s--; t--;
scanf("%d%d", &a, &b); a--; b--;
G.resize(N); Dinit.resize(N); Dtrans.resize(N); E.resize(M);
for (int i = 0; i < M; i++) {
int u, v, d;
scanf("%d%d%d", &u, &v, &d); u--; v--;
G[u].push_back(make_pair(v, d));
G[v].push_back(make_pair(u, d));
E[i].x = u; E[i].y = v; E[i].len = d;
}
Dijkstra(s, N, Dinit);
Dijkstra(t, N, Dtrans);
if (N > 300) { solve_large(N, M, t, a, b); return 0; }
vector<long long> Da(N), Db(N);
Dijkstra(a, N, Da);
Dijkstra(b, N, Db);
long long res = Da[b];
for (int i = 0; i < N; i++) G[i].resize(0);
for (int i = 0; i < M; i++) {
int u = E[i].x, v = E[i].y, d = E[i].len;
if (Dinit[u] + Dtrans[v] + d == Dinit[t])
G[u].push_back(make_pair(v, 0)); // direction u -> v, no cost
else if (Dinit[v] + Dtrans[u] + d == Dinit[t])
G[v].push_back(make_pair(u, 0)); // direction v -> u, no cost
}
vector <long long> Ddag(N);
for (int x=0; x<N; x++) {
if (Dinit[x] + Dtrans[x] != Dinit[t]) continue;
Dijkstra(x, N, Ddag);
for (int y=0; y<N; y++) {
if (Ddag[y] == INF) continue;
res = min(res, min(Da[x]+Db[y], Db[x]+Da[y]));
}
}
printf("%lld\n", res);
return 0;
}
