#include <bits/stdc++.h>
using namespace std;
typedef pair <int, int> ii;
typedef pair <long long, long long> ll;
#define INF 1000000000000000000
int n, m;
int s, t;
int u, v;
vector <ii> adjList[200005], adjList1[200005], adjList2[200005];
long long distu[100005], distv[100005], dists[100005], distt[100005];
long long ans;
priority_queue<ll, vector<ii>, greater<ii> > pq;
void dijkstra(int a, long long *dist) {
for (int i = 1; i <= n; i++) dist[i] = INF;
dist[a] = 0;
pq.emplace(0, a);
while (!pq.empty()) {
int u, d; tie(d, u) = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (ii vw : adjList[u]) {
int v, w; tie(v, w) = vw;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.emplace(dist[v], v);
}
}
}
}
long long memo[100005][2];
long long dp(int i, bool stt) {
if (memo[i][stt] != -1) return memo[i][stt];
if (i == v) return 0;
memo[i][stt] = INF;
for (ii vw : adjList[i]) {
int v, w; tie(v, w) = vw;
if ((stt && dists[i] + distt[v] + w == dists[t]) || (!stt && dists[v] + distt[i] + w == dists[t]))
memo[i][stt] = min(memo[i][stt], dp(v, stt));
else memo[i][stt] = min(memo[i][stt], distv[v] + w);
}
return memo[i][stt];
}
int main() {
scanf("%d%d", &n, &m);
scanf("%d%d", &s, &t);
scanf("%d%d", &u, &v);
for (int i = 0; i < m; i++) {
int a, b, c; scanf("%d%d%d", &a, &b, &c);
adjList[a].emplace_back(b, c);
adjList[b].emplace_back(a, c);
}
dijkstra(u, distu);
dijkstra(v, distv);
dijkstra(s, dists);
dijkstra(t, distt);
ans = distu[v];
memset(memo, -1, sizeof memo);
for (int i = 1; i <= n; i++) {
if (dists[i] + distt[i] == dists[t]) {
ans = min(ans, distu[i] + min(dp(i, true), dp(i, false)));
}
}
printf("%lld\n", ans);
return 0;
}
