#include <bits/stdc++.h>
using namespace std;
int n, m;
int a, b, c, d;
vector<array<int, 3>> g[100005];
int u[200005];
int v[200005];
int w[200005];
long long da[100005];
long long db[100005];
bool ok[200005];
long long dd[100005][3];
void dijkstra_a() {
memset(da, 0x3f, sizeof(da));
da[a] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
pq.push(make_pair(da[a], a));
while (!pq.empty()) {
long long cd = pq.top().first;
int node = pq.top().second;
pq.pop();
if (cd != da[node]) {
continue;
}
for (int i = 0; i < (int) g[node].size(); i++) {
int nxt = g[node][i][0];
int wt = g[node][i][1];
if (da[nxt] > da[node] + wt) {
da[nxt] = da[node] + wt;
pq.push(make_pair(da[nxt], nxt));
}
}
}
}
void dijkstra_b() {
memset(db, 0x3f, sizeof(db));
db[b] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
pq.push(make_pair(db[b], b));
while (!pq.empty()) {
long long cd = pq.top().first;
int node = pq.top().second;
pq.pop();
if (cd != db[node]) {
continue;
}
for (int i = 0; i < (int) g[node].size(); i++) {
int nxt = g[node][i][0];
int wt = g[node][i][1];
if (db[nxt] > db[node] + wt) {
db[nxt] = db[node] + wt;
pq.push(make_pair(db[nxt], nxt));
}
}
}
}
long long dijkstra(int src, int dst) {
memset(dd, 0x3f, sizeof(dd));
dd[src][0] = 0;
priority_queue<pair<long long, pair<int, int>>, vector<pair<long long, pair<int, int>>>, greater<pair<long long, pair<int, int>>>> pq;
pq.push(make_pair(dd[src][0], make_pair(src, 0)));
while (!pq.empty()) {
long long cd = pq.top().first;
int node = pq.top().second.first;
int state = pq.top().second.second;
pq.pop();
if (cd != dd[node][state]) {
continue;
}
for (int i = 0; i < (int) g[node].size(); i++) {
int nxt = g[node][i][0];
int wt = g[node][i][1];
int eid = g[node][i][2];
if (state <= 0) {
if (dd[nxt][0] > cd + wt) {
dd[nxt][0] = cd + wt;
pq.push(make_pair(dd[nxt][0], make_pair(nxt, 0)));
}
}
if (state <= 1) {
if (ok[eid] && da[nxt] == da[node] + wt && dd[nxt][1] > cd) {
dd[nxt][1] = cd;
pq.push(make_pair(dd[nxt][1], make_pair(nxt, 1)));
}
}
if (state <= 2) {
if (dd[nxt][2] > cd + wt) {
dd[nxt][2] = cd + wt;
pq.push(make_pair(dd[nxt][2], make_pair(nxt, 2)));
}
}
}
}
return min(dd[dst][0], min(dd[dst][1], dd[dst][2]));
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m;
cin >> a >> b >> c >> d;
for (int i = 1; i <= m; i++) {
cin >> u[i] >> v[i] >> w[i];
g[u[i]].push_back(array<int, 3>{v[i], w[i], i});
g[v[i]].push_back(array<int, 3>{u[i], w[i], i});
}
dijkstra_a();
dijkstra_b();
for (int i = 1; i <= m; i++) {
ok[i] |= (da[u[i]] + w[i] + db[v[i]] == da[b]);
ok[i] |= (da[v[i]] + w[i] + db[u[i]] == da[b]);
}
cout << min(dijkstra(c, d), dijkstra(d, c));
return 0;
}
