#include <iostream>
#include <vector>
#include <queue>
#define int int64_t
using namespace std;
struct graph
{
int n;
vector<vector<pair<int,int>>> adjlist;
vector<int> svs;
vector<int> mto;
vector<int> dist;
void dijkstra(int st)
{
priority_queue<pair<int,pair<int,int>>> pq;
pq.emplace(0, make_pair(st, st));
mto = svs;
dist.assign(n, 1e17);
while (!pq.empty())
{
auto [tm, nf] = pq.top();
auto [curr, par] = nf;
pq.pop();
tm = -tm;
if (dist[curr] >= tm) mto[curr] = min(mto[curr], mto[par]);
if (dist[curr] <= tm) continue;
dist[curr] = tm;
// cerr << curr << " " << tm << "\n";
for (auto np : adjlist[curr])
{
pq.emplace(-(np.second + tm), make_pair(np.first, curr));
}
}
}
};
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
s--; t--; u--; v--;
graph g;
g.n = n;
g.adjlist.resize(n);
g.dist.resize(n, 1e17);
g.svs.resize(n, 1e17);
g.mto.resize(n);
for (int i = 0; i < m; i++)
{
int a, b, c;
cin >> a >> b >> c;
a--; b--;
g.adjlist[a].emplace_back(b, c);
g.adjlist[b].emplace_back(a, c);
}
g.dijkstra(s);
vector<int> frs = g.dist;
int dst = g.dist[t];
g.dijkstra(t);
vector<int> frt = g.dist;
g.dijkstra(u);
int mmin = g.dist[v];
auto calc = [&](int a, int b)
{
// cerr << a << "\n";
g.dijkstra(a);
g.svs = g.dist;
for (int i = 0; i < n; i++)
{
// cerr << g.svs[i] << " ";
}
// cerr << "\n";
for (int i = 0; i < n; i++)
{
// cerr << g.dist[i] << " ";
}
// cerr << "\n";
g.dijkstra(t);
auto crs = g.mto;
g.dijkstra(b);
for (int i = 0; i < n; i++)
{
if (frs[i] + frt[i] == dst)
{
mmin = min(mmin, g.dist[i] + crs[i]);
}
}
};
calc(u, v);
calc(v, u);
cout << mmin << "\n";
}
