#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair <LL, int> PLLI;
typedef pair <LL, pair <int, int> > PLLII;
constexpr int NMAX = 1e5 + 5;
constexpr LL INF = 1LL * 1e17;
int N, M, S, T, U, V;
vector <PLLI> G[NMAX];
LL Dist_U[NMAX];
LL Dist_V[NMAX];
bool viz[NMAX];
LL ans = INF;
LL Dist[2][NMAX];
LL dp[2][NMAX];
void Dijkstra (int start, LL who[]) {
memset(viz, 0, sizeof(viz));
for (int i = 1; i <= N; ++ i )
who[i] = -1;
priority_queue <PLLI, vector <PLLI>, greater <PLLI> > H;
H.push({0, start});
while (!H.empty()) {
int node = H.top().second;
LL cost = H.top().first;
H.pop();
if (viz[node]) continue;
viz[node] = true;
who[node] = cost;
for (auto it : G[node]) {
H.push({cost + it.first, it.second});
}
}
}
LL Total_Dist[NMAX];
void Answer (int st, int en) {
memset(viz, 0, sizeof(viz));
memset(Total_Dist, 0, sizeof(Total_Dist));
for (int i = 1; i <= N; ++ i ) {
Total_Dist[i] = INF;
for (int j = 0; j < 2; ++ j )
dp[j][i] = 0;
}
priority_queue <PLLII, vector <PLLII>, greater <PLLII> > H;
dp[0][0] = dp[1][0] = INF;
H.push({0, {st, 0}});
while (!H.empty()) {
LL cost = H.top().first;
int node = H.top().second.first;
int parent = H.top().second.second;
H.pop();
if (viz[node]) {
if (Total_Dist[node] < cost) continue;
LL to[2];
for (int j = 0; j < 2; ++ j )
to[j] = min(dp[j][parent], Dist[j][node]);
if (to[0] + to[1] <= dp[0][node] + dp[1][node]) {
for (int j = 0; j < 2; ++ j )
dp[j][node] = to[j];
}
continue;
}
viz[node] = true;
Total_Dist[node] = cost;
for (int j = 0; j < 2; ++ j )
dp[j][node] = min(dp[j][parent], Dist[j][node]);
for (auto it : G[node])
H.push({cost + it.first, {it.second, node}});
}
ans = min(ans, dp[0][en] + dp[1][en]);
}
int main () {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> N >> M >> S >> T >> U >> V;
for (int i = 1; i <= M; ++ i ) {
int x, y;
LL c;
cin >> x >> y >> c;
G[x].push_back({c, y});
G[y].push_back({c, x});
}
Dijkstra(U, Dist[0]);
Dijkstra(V, Dist[1]);
ans = Dist[0][V];
Answer(S, T);
Answer(T, S);
cout << ans << '\n';
return 0;
}
