#include <bits/stdc++.h>
using namespace std;
#define int long long
const int INF = (int) (1e18);
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int n, m; cin >> n >> m;
int s, t, u, v; cin >> s >> t >> u >> v;
vector<pair<int, int>> adja[n + 1];
vector<int> distanceCur(n + 1, 0);
vector<int> distanceS(n + 1, 0);
vector<int> distanceT(n + 1, 0);
vector<int> distanceU(n + 1, 0);
vector<int> distanceV(n + 1, 0);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for (int i = 1; i <= m; i ++) {
int dest, dep, pds; cin >> dest >> dep >> pds;
adja[dest].push_back({dep, pds});
adja[dep].push_back({dest, pds});
}
// destination, puis poids
distanceCur.assign(n + 1, INF);
distanceCur[s] = 0;
pq.push({0, s});
while (! pq.empty()) {
auto som = pq.top();
pq.pop();
if (som.first != distanceCur[som.second])
continue;
for (auto voisin : adja[som.second]) {
if (distanceCur[voisin.first] > voisin.second + som.first) {
distanceCur[voisin.first] = voisin.second + som.first;
pq.push({distanceCur[voisin.first], voisin.first});
}
}
}
distanceS = distanceCur;
distanceCur.assign(n + 1, INF);
distanceCur[t] = 0;
pq.push({0, t});
while (! pq.empty()) {
auto som = pq.top();
pq.pop();
if (som.first != distanceCur[som.second])
continue;
for (auto voisin : adja[som.second]) {
if (distanceCur[voisin.first] > voisin.second + som.first) {
distanceCur[voisin.first] = voisin.second + som.first;
pq.push({distanceCur[voisin.first], voisin.first});
}
}
}
distanceT = distanceCur;
distanceCur.assign(n + 1, INF);
distanceCur[u] = 0;
pq.push({0, u});
while (! pq.empty()) {
auto som = pq.top();
pq.pop();
if (som.first != distanceCur[som.second])
continue;
for (auto voisin : adja[som.second]) {
if (distanceCur[voisin.first] > voisin.second + som.first) {
distanceCur[voisin.first] = voisin.second + som.first;
pq.push({distanceCur[voisin.first], voisin.first});
}
}
}
distanceU = distanceCur;
distanceCur.assign(n + 1, INF);
distanceCur[v] = 0;
pq.push({0, v});
while (! pq.empty()) {
auto som = pq.top();
pq.pop();
if (som.first != distanceCur[som.second])
continue;
for (auto voisin : adja[som.second]) {
if (distanceCur[voisin.first] > voisin.second + som.first) {
distanceCur[voisin.first] = voisin.second + som.first;
pq.push({distanceCur[voisin.first], voisin.first});
}
}
}
distanceV = distanceCur;
int ans = distanceU[v];
vector<int> distanceSU(n + 1, INF);
vector<int> distanceSV(n + 1, INF);
vector<int> distanceTU(n + 1, INF);
vector<int> distanceTV(n + 1, INF);
for (int i = 1; i <= n; i ++) {
distanceSU[i] = distanceU[i];
distanceTU[i] = distanceU[i];
distanceSV[i] = distanceV[i];
distanceTV[i] = distanceV[i];
}
vector<pair<int, int>> SU;
for (int i = 1; i <= n; i ++) {
SU.push_back({distanceS[i], i});
}
sort(SU.begin(), SU.end());
for (int i = 0; i < n; i ++) {
int node = SU[i].second;
for (auto voi : adja[node]) {
if (distanceS[voi.first] + voi.second == distanceS[node])
distanceSU[node] = min(distanceSU[node], distanceSU[voi.first]);
}
}
vector<pair<int, int>> SV;
for (int i = 1; i <= n; i ++) {
SV.push_back({distanceS[i], i});
}
sort(SV.begin(), SV.end());
for (int i = 0; i < n; i ++) {
int node = SV[i].second;
for (auto voi : adja[node]) {
if (distanceS[voi.first] + voi.second == distanceS[node])
distanceSV[node] = min(distanceSV[node], distanceSV[voi.first]);
}
}
vector<pair<int, int>> TU;
for (int i = 1; i <= n; i ++) {
TU.push_back({distanceT[i], i});
}
sort(TU.begin(), TU.end());
for (int i = 0; i < n; i ++) {
int node = TU[i].second;
for (auto voi : adja[node]) {
if (distanceT[voi.first] + voi.second == distanceT[node])
distanceTU[node] = min(distanceTU[node], distanceTU[voi.first]);
}
}
vector<pair<int, int>> TV;
for (int i = 1; i <= n; i ++) {
TV.push_back({distanceT[i], i});
}
sort(TV.begin(), TV.end());
for (int i = 0; i < n; i ++) {
int node = TV[i].second;
for (auto voi : adja[node]) {
if (distanceT[voi.first] + voi.second == distanceT[node])
distanceTV[node] = min(distanceTV[node], distanceTV[voi.first]);
}
}
for (int w = 1; w <= n; w ++) {
if (distanceS[w] + distanceT[w] == distanceS[t]) {
ans = min(ans, distanceSU[w] + distanceTV[w]);
ans = min(ans, distanceSV[w] + distanceTU[w]);
}
}
cout << ans << '\n';
}
