#include<stdio.h>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
#define MAXN 100005
#define MAXM 200005
typedef long long lint;
typedef pair<lint, int> pli;
const lint LINF = 1ll << 50;
int N, M, S, T, U, V;
int A[MAXM], B[MAXM];
lint C[MAXM];
vector<pli> ed[MAXN];
priority_queue<pli> pq;
lint disS[MAXN], disT[MAXN], disU[MAXN], disV[MAXN];
vector<int> sho;
lint dp[MAXN];
lint ans;
void dij(int x, lint dis[]) {
pq.push(make_pair(0ll, x));
for(int i = 1; i <= N; i++) dis[i] = LINF;
dis[x] = 0ll;
while(!pq.empty()) {
pli t = pq.top();
pq.pop();
if(dis[t.second] != t.first) continue;
for(auto a : ed[t.second]) if(t.first + a.first < dis[a.second]) {
dis[a.second] = t.first + a.first;
pq.push(make_pair(dis[a.second], a.second));
}
}
}
void solve(int U, int V, lint disU[], lint disV[]) {
for(auto a : sho) {
dp[a] = disU[a];
for(auto b : ed[a]) if(disS[b.second] + disT[b.second] == disS[T] && disS[b.second] < disS[a])
dp[a] = min(dp[a], dp[b.second]);
ans = min(ans, dp[a] + disV[a]);
}
}
int main() {
scanf("%d%d%d%d%d%d", &N, &M, &S, &T, &U, &V);
for(int i = 0; i < M; i++) scanf("%d%d%lld", A + i, B + i, C + i);
for(int i = 0; i < M; i++) {
ed[A[i]].push_back(make_pair(C[i], B[i]));
ed[B[i]].push_back(make_pair(C[i], A[i]));
}
dij(S, disS);
dij(T, disT);
dij(U, disU);
dij(V, disV);
for(int i = 1; i <= N; i++) if(disS[i] + disT[i] == disS[T]) sho.push_back(i);
sort(sho.begin(), sho.end(), [&](const int &a, const int &b) { return disS[a] < disS[b]; } );
ans = disU[V];
solve(U, V, disU, disV);
solve(V, U, disV, disU);
printf("%lld", ans);
return 0;
}
