#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
const long long oo = 1e18;
int n, m, s1, t1, s2, t2;
vector<pair<int, long long>> adj[N];
long long ds[N], dt[N], dd[N][3];
void Dijkstra(int st, long long d[]) {
for (int u = 1; u <= n; u++) d[u] = oo;
d[st] = 0;
priority_queue<pair<long long, int>> pq;
pq.emplace(0, st);
while (pq.size()) {
int u; long long di; tie(di, u) = pq.top();
di = -di;
pq.pop();
if (d[u] != di) continue;
for (auto V: adj[u]) {
int v; long long w; tie(v, w) = V;
if (d[v] > di + w) {
pq.emplace(-(d[v] = di + w), v);
}
}
}
}
void Dijkstra21(void) {
for (int u = 1; u <= n; u++) dd[u][0] = dd[u][1] = dd[u][2] = oo;
dd[s2][0] = 0;
priority_queue<pair<long long, pair<int, int>>> pq;
pq.push({0, {s2, 0}});
while (pq.size()) {
int u = pq.top().second.first, b = pq.top().second.second; long long di = -pq.top().first;
pq.pop();
if (dd[u][b] != di) continue;
if (b < 2) {
if (dd[u][b + 1] > di) {
pq.push({-(dd[u][b + 1] = di), {u, b + 1}});
}
}
for (auto V: adj[u]) {
int v; long long w; tie(v, w) = V;
if (b != 1) {
if (dd[v][b] > di + w) {
pq.push({-(dd[v][b] = di + w), {v, b}});
}
} else {
if (ds[u] + w + dt[v] == ds[t1] && dd[v][1] > di) {
pq.push({-(dd[v][1] = di), {v, 1}});
}
}
}
}
}
void Dijkstra22(void) {
for (int u = 1; u <= n; u++) dd[u][0] = dd[u][1] = dd[u][2] = oo;
dd[s2][0] = 0;
priority_queue<pair<long long, pair<int, int>>> pq;
pq.push({0, {s2, 0}});
while (pq.size()) {
int u = pq.top().second.first, b = pq.top().second.second; long long di = -pq.top().first;
pq.pop();
if (dd[u][b] != di) continue;
if (b < 2) {
if (dd[u][b + 1] > di) {
pq.push({-(dd[u][b + 1] = di), {u, b + 1}});
}
}
for (auto V: adj[u]) {
int v; long long w; tie(v, w) = V;
if (b != 1) {
if (dd[v][b] > di + w) {
pq.push({-(dd[v][b] = di + w), {v, b}});
}
} else {
if (ds[v] + w + dt[u] == ds[t1] && dd[v][1] > di) {
pq.push({-(dd[v][1] = di), {v, 1}});
}
}
}
}
}
void solve(void) {
cin >> n >> m >> s1 >> t1 >> s2 >> t2;
for (int i = 1, a, b, w; i <= m; i++) {
cin >> a >> b >> w;
adj[a].emplace_back(b, w);
adj[b].emplace_back(a, w);
}
Dijkstra(s1, ds); Dijkstra(t1, dt);
long long ans = oo;
Dijkstra21(); ans = min(ans, dd[t2][2]);
Dijkstra22(); ans = min(ans, dd[t2][2]);
cout << ans;
}
signed main(void) {
ios::sync_with_stdio(false); cin.tie(nullptr);
int TEST = 1;
while (TEST--) solve();
return 0;
}
