#include <cstdio>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
#define f first
#define s second
#define ll long long
#define pii pair<int, int>
#define pli pair<ll, int>
const int MAX_N = 100001;
long long dists[MAX_N], distt[MAX_N], distu[MAX_N], distv[MAX_N], dp[MAX_N], dp2[MAX_N], res = 1e18;
vector<pii> edges[MAX_N];
vector<int> bef[MAX_N], bef2[MAX_N];
void dijkstra(int s, ll dist[]) {
for (int i=0; i<MAX_N; i++) dist[i] = 1e18;
dist[s] = 0;
priority_queue<pli, vector<pli>, greater<pli> > pq;
pq.push({0, s});
while (!pq.empty()) {
pli cur = pq.top();
pq.pop();
if (cur.f > dist[cur.s]) continue;
for (pii p : edges[cur.s]) {
if (dist[p.f] > dist[cur.s]+p.s) {
dist[p.f] = dist[cur.s]+p.s;
pq.push({dist[p.f], p.f});
}
}
}
}
ll ans(int x, vector<int> bef[], ll dp[]) {
if (dp[x] != 1e18) return dp[x];
dp[x]--;
for (int p : bef[x]) dp[x] = min(dp[x], ans(p, bef, dp));
return dp[x] = min(dp[x], distu[x]);
}
int main() {
int n, m, s, t, u, v, a, b, c;
scanf("%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
while (m--) {
scanf("%d%d%d", &a, &b, &c);
edges[a].emplace_back(b, c);
edges[b].emplace_back(a, c);
}
dijkstra(s, dists);
dijkstra(t, distt);
dijkstra(u, distu);
dijkstra(v, distv);
for (int i=1; i<=n; i++) {
for (pii j : edges[i]) {
if (dists[i]+j.s+distt[j.f] == dists[t]) {
bef[j.f].push_back(i);
bef2[i].push_back(j.f);
}
}
dp[i] = dp2[i] = 1e18;
}
for (int i=1; i<=n; i++) {
if (dists[i]+distt[i]==dists[t]) {
res = min(res, min(ans(i, bef, dp), ans(i, bef2, dp2))+distv[i]);
}
}
printf("%lld\n", min(res, distu[v]));
}
