#include<bits/stdc++.h>
using namespace std;
using i64 = int64_t;
vector<vector<pair<i64, i64>>> con;
void Dijkstra(vector<i64>& dij, i64 pocz, i64 N)
{
priority_queue<pair<i64, i64>, vector<pair<i64, i64>>, greater<pair<i64, i64>>> Q;
Q.push({0, pocz});
vector<bool> bylo(N);
while (!Q.empty())
{
pair<i64, i64> akt = Q.top();
Q.pop();
if (bylo[akt.second])
{
continue;
}
bylo[akt.second] = true;
dij[akt.second] = akt.first;
for (int i = 0; i < con[akt.second].size(); i++)
{
Q.push({akt.first + con[akt.second][i].second, con[akt.second][i].first});
}
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
i64 N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
S--;
T--;
U--;
V--;
con.resize(N);
for (int i = 0; i < M; i++)
{
i64 a, b, c;
cin >> a >> b >> c;
a--;
b--;
con[a].push_back({b, c});
con[b].push_back({a, c});
}
vector<i64> dis(N), dit(N), div(N), diu(N);
Dijkstra(dis, S, N);
Dijkstra(dit, T, N);
Dijkstra(div, V, N);
Dijkstra(diu, U, N);
i64 wynik = diu[V], minn = dis[T];
vector<pair<i64, i64>> kopu(N);
for (int i = 0; i < N; i++)
{
kopu[i] = {diu[i], i};
}
sort(kopu.begin(), kopu.end());
vector<bool> bylo(N);
for (int i = 0; i < N; i++)
{
i64 poz = kopu[i].second;
if (dis[poz] + dit[poz] == minn && !bylo[poz])
{
queue<i64> Q;
Q.push(poz);
while (!Q.empty())
{
int akt = Q.front();
Q.pop();
if (bylo[akt])
{
continue;
}
bylo[akt] = true;
wynik = min(wynik, div[akt] + kopu[i].first);
for (int k = 0; k < con[akt].size(); k++)
{
int next = con[akt][k].first, cost = con[akt][k].second;
if (dis[next] == dis[akt] - cost && dit[next] == dit[akt] + cost)
{
Q.push(next);
}
}
}
}
}
for (int i = 0; i < N; i++)
{
bylo[i] = false;
}
for (int i = 0; i < N; i++)
{
i64 poz = kopu[i].second;
if (dis[poz] + dit[poz] == minn && !bylo[poz])
{
queue<i64> Q;
Q.push(poz);
while (!Q.empty())
{
int akt = Q.front();
Q.pop();
if (bylo[akt])
{
continue;
}
bylo[akt] = true;
wynik = min(wynik, div[akt] + kopu[i].first);
for (int k = 0; k < con[akt].size(); k++)
{
int next = con[akt][k].first, cost = con[akt][k].second;
if (dis[next] == dis[akt] + cost && dit[next] == dit[akt] - cost)
{
Q.push(next);
}
}
}
}
}
cout << wynik << "\n";
return 0;
}
