#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF = 1e18;
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
--s;
--t;
--u;
--v;
vector<vector<pair<int, ll>>> adjacency(n);
for (int i = 0; i < m; ++i) {
int a, b;
ll c;
cin >> a >> b >> c;
--a;
--b;
adjacency[a].emplace_back(b, c);
adjacency[b].emplace_back(a, c);
}
auto dijkstra1 = [&](int start, vector<ll> &dist) {
dist.assign(n, INF);
priority_queue<pair<ll, int>> pq;
pq.emplace(0, start);
dist[start] = 0;
while (!pq.empty()) {
auto [curDist, cur] = pq.top();
pq.pop();
curDist = -curDist;
if (curDist != dist[cur]) continue;
for (auto &[adj, len] : adjacency[cur]) {
if (dist[adj] > curDist + len) {
dist[adj] = curDist + len;
pq.emplace(-curDist - len, adj);
}
}
}
};
vector<ll> distU(n), distV(n);
dijkstra1(u, distU);
dijkstra1(v, distV);
ll ans = distU[v];
auto dijkstra2 = [&](int start, int end) {
vector<ll> dp0(n, INF), dp1(n, INF), dist(n, INF);
vector<bool> visited(n, false);
priority_queue<pair<ll, pair<int, int>>> pq;
dist[start] = 0;
pq.push({0, {start, 0}});
while (!pq.empty()) {
auto [curDist, curPar] = pq.top();
pq.pop();
if (!visited[curPar.first]) {
visited[curPar.first] = true;
dist[curPar.first] = -curDist;
dp0[curPar.first] =
min(distU[curPar.first], dp0[curPar.second]);
dp1[curPar.first] =
min(distV[curPar.first], dp1[curPar.second]);
for (auto &[adj, len] : adjacency[curPar.first])
pq.push({curDist - len, {adj, curPar.first}});
} else if (-curDist == dist[curPar.first]) {
if (min(distU[curPar.first], dp0[curPar.second]) +
min(distV[curPar.first], dp1[curPar.second]) <
dp0[curPar.first] + dp1[curPar.first]) {
dp0[curPar.first] =
min(distU[curPar.first], dp0[curPar.second]);
dp1[curPar.first] =
min(distV[curPar.first], dp1[curPar.second]);
}
}
}
ans = min(ans, dp0[end] + dp1[end]);
};
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans << '\n';
return 0;
}
