#include <algorithm>
#include <iostream>
#include <vector>
#include <limits>
#include <queue>
using namespace std;
typedef long long ll;
ll N, M, S, T, U, V, dist[5][100005];
bool good[100005];
pair<ll, ll> best[100005];
vector<pair<ll, ll>> routes[100005];
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
void dk(ll s, ll id) {
fill(begin(dist[id]), end(dist[id]), numeric_limits<int>::max());
dist[id][s] = 0;
pq.push({ 0, s });
while (!pq.empty()) {
auto curr = pq.top();
pq.pop();
if (curr.first > dist[id][curr.second]) continue;
for (auto child : routes[curr.second]) {
if (child.first + curr.first < dist[id][child.second]) {
dist[id][child.second] = child.first + curr.first;
pq.push({ dist[id][child.second], child.second });
}
}
}
}
ll solve() {
fill(begin(dist[3]), end(dist[3]), numeric_limits<int>::max());
ll output = dist[1][S] + dist[2][S];
dist[3][S] = dist[1][S];
pq.push({ 0, S });
while (!pq.empty()) {
auto curr = pq.top();
pq.pop();
if (curr.first > dist[3][curr.second]) continue;
for (auto child : routes[curr.second]) {
if (dist[0][child.second] + child.first == dist[0][curr.second]) {
int newD = min(dist[1][child.second], dist[3][curr.second]);
if (newD < dist[3][child.second]) {
output = min(output, newD + dist[2][child.second]);
dist[3][child.second] = newD;
pq.push({ newD, child.second });
}
}
}
}
return output;
}
int main() {
cin.tie(0); ios::sync_with_stdio(0);
cin >> N >> M >> S >> T >> U >> V;
ll a, b, c;
for (ll i = 0; i < M; ++i) {
cin >> a >> b >> c;
routes[a].push_back({ c, b });
routes[b].push_back({ c, a });
}
// dist[0] = nuke path
// dist[1] = distances to U
// dist[2] = distances to V
// dist[3] = u_x to u + v_x to v (1 then 2 or 2 then 1)
dk(T, 0);
dk(U, 1);
dk(V, 2);
ll ans = solve();
dk(U, 2);
dk(V, 1);
cout << min(ans, solve());
//cout << ans << " " << solve();
}
