#include <iostream>
#include <vector>
#include <queue>
#include <tuple>
#include <unordered_set>
#include <cstring>
#define inf 1'000'000'000'000
#define int long long
using namespace std;
typedef pair<int, int> ii;
vector<pair<int, int>> graf[100005];
vector<int> par[100005];
pair<int, int> dp[100005];
void dij(int st, vector<int>& dist, bool dg = false)
{
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.push({0, st});
dist[st] = 0;
while (!pq.empty())
{
auto [d, u] = pq.top();
pq.pop();
if (d > dist[u])
continue;
for (auto [v, w] : graf[u])
{
if (dist[v] != -1 && d+w > dist[v])
continue;
if (dg)
{
if (d+w == dist[v])
{
par[v].push_back(u);
continue;
}
par[v].clear();
par[v].push_back(u);
// cout << u << "->" << v << "\n";
}
else if (d+w == dist[v])
continue;
dist[v] = d+w;
pq.push({dist[v], v});
}
}
}
int gl = 0;
pair<int, int> dfs(vector<int>& dist1, vector<int>& dist2, int vz)
{
if (dp[vz].first != 0)
return dp[vz];
pair<int, int> rez = {dist1[vz], dist2[vz]};
for (int v : par[vz])
{
gl++;
auto[nu, nv] = dfs(dist1, dist2, v);
gl--;
if (nu < rez.first)
{
rez.first = nu;
rez.second = min(dist2[vz], nv);
}
else if (nv < rez.second)
{
rez.second = nv;
rez.first = min(dist1[vz], nu);
}
}
return dp[vz] = rez;
}
int32_t main()
{
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
for (int i = 0; i < m; i++)
{
int u, v, w;
cin >> u >> v >> w;
graf[u].push_back({v, w});
graf[v].push_back({u, w});
}
vector<int> dist2(n+1, -1);
vector<int> dist3(n+1, -1);
dij(s, dist2, true);
fill(dist2.begin(), dist2.end(), -1);
dij(u, dist2);
dij(v, dist3);
int rez = dist2[v];
pair<int, int> par = dfs(dist2, dist3, t);
cout << min(rez, par.first+par.second) << "\n";
// for (int i = 1; i <= n; i++)
// cout << dp[i].first << " " << dp[i].second << "\n";
return 0;
}
