#include <bits/stdc++.h>
#define FR(i, N) for (int i = 0; i < int(N); i++)
#define all(x) begin(x), end(x)
#define f first
#define s second
using namespace std;
using ll = long long;
const int MAXN = 100000;
vector<pair<int, int>> adj[MAXN];
const ll INF = (ll)(1e18);
int N, M;
int pass[2];
ll dist[4][MAXN];
ll distPass[2][MAXN];
int start, stop;
void dijkstraPass(int s) {
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
FR(i, MAXN) {
distPass[s][i] = INF;
}
distPass[s][pass[s]] = 0;
pq.push({0, pass[s]});
while (pq.size()) {
auto [d, n] = pq.top();
pq.pop();
if (distPass[s][n] == d) {
for (auto [e, w] : adj[n]) {
if (distPass[s][e] > distPass[s][n] + w) {
distPass[s][e] = distPass[s][n] + w;
pq.push({distPass[s][e], e});
}
}
}
}
}
int main() {
cin.tie(0);
cin.sync_with_stdio(0);
cin >> N >> M;
cin >> pass[0] >> pass[1];
cin >> start >> stop;
pass[0]--, pass[1]--, start--, stop--;
FR(i, M) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijkstraPass(0);
dijkstraPass(1);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
FR(i, 4) FR(j, MAXN) dist[i][j] = INF;
dist[0][start] = 0;
pq.push({0, start});
ll minDist = distPass[0][pass[1]];
while (pq.size()) {
auto[d, n] = pq.top();
pq.pop();
int state = n/N;
n%=N;
if (dist[state][n] == d) {
if (state == 0 || state == 3) {
for (auto [e, w] : adj[n]) {
if (dist[state][e] > dist[state][n] + w) {
dist[state][e] = dist[state][n] + w;
pq.push({dist[state][e], state*N + e});
}
}
}
if (state == 0) {
for (auto [e, w] : adj[n]) {
if (distPass[0][n] + distPass[1][e] + w == minDist && dist[2][e] > d) {
dist[2][e] = d;
pq.push({d, 2*N + e});
}
if (distPass[1][n] + distPass[0][e] + w == minDist && dist[1][e] > d) {
dist[1][e] = d;
pq.push({d, N + e});
}
}
}
if (state == 1 || state == 2) {
for (auto [e, w] : adj[n]) {
if ((state == 1 ? distPass[1][n] + distPass[0][e] + w : distPass[0][n] + distPass[1][e] + w) == minDist && dist[state][e] > d) {
dist[state][e] = d;
pq.push({d, state*N + e});
}
}
}
if (dist[3][n] > d) {
pq.push({d, 3*N + n});
dist[3][n] = d;
}
}
}
cout << dist[3][stop] << '\n';
return 0;
}
