#include <bits/stdc++.h>
using namespace std;
size_t n, m;
vector<vector<pair<unsigned, int64_t>>> g;
void dijkstra(unsigned s, vector<int64_t> &dis, vector<vector<unsigned>> *pre = 0)
{
priority_queue<pair<int64_t, unsigned>, vector<pair<int64_t, unsigned>>, greater<pair<int64_t, unsigned>>> q;
q.push({0, s});
dis[s] = 0;
while (!q.empty())
{
auto const [z, u] = q.top();
q.pop();
if (dis[u] != z)
continue;
for (auto const &[v, w] : g[u])
{
if (z + w < dis[v])
{
dis[v] = z + w;
q.push({z + w, v});
if (pre)
{
(*pre)[v].clear();
(*pre)[v].push_back(u);
}
}
else if (z + w == dis[v] && pre)
{
(*pre)[v].push_back(u);
}
}
}
}
int64_t min_cost(
unsigned s, unsigned t, unsigned x, unsigned y,
vector<int64_t> const &s_dis, vector<vector<unsigned>> const &s_pre,
vector<int64_t> const &x_dis, vector<int64_t> const &y_dis)
{
vector<int64_t> min_y_dis(n);
for (unsigned u = 0; u < n; u++)
min_y_dis[u] = y_dis[u];
vector<bool> vis(n, 0);
vis[t] = 1;
int64_t min_total = INT64_MAX;
priority_queue<pair<int64_t, unsigned>, vector<pair<int64_t, unsigned>>, greater<pair<int64_t, unsigned>>> q;
q.push({min_y_dis[t], t});
while (!q.empty())
{
auto const [z, u] = q.top();
q.pop();
if (z != min_y_dis[u])
continue;
min_total = min(min_total, min_y_dis[u] + x_dis[u]);
for (unsigned v : s_pre[u])
{
min_y_dis[v] = min(min_y_dis[v], min_y_dis[u]);
q.push({min_y_dis[v], v});
}
}
return min_total;
}
int main()
{
cin >> n >> m;
unsigned s, t, x, y;
cin >> s >> t >> x >> y;
s--, t--, x--, y--;
g = vector<vector<pair<unsigned, int64_t>>>(n);
for (size_t i = 0; i < m; i++)
{
unsigned u, v;
int64_t w;
cin >> u >> v >> w;
g[u - 1].push_back({v - 1, w});
g[v - 1].push_back({u - 1, w});
}
vector<int64_t> x_dis(n, INT64_MAX), y_dis(n, INT64_MAX);
dijkstra(x, x_dis);
dijkstra(y, y_dis);
vector<int64_t> s_dis(n, INT64_MAX);
vector<vector<unsigned>> s_pre(n);
dijkstra(s, s_dis, &s_pre);
cout << min(x_dis[y], min(min_cost(s, t, x, y, s_dis, s_pre, x_dis, y_dis),
min_cost(s, t, y, x, s_dis, s_pre, y_dis, x_dis)))
<< '\n';
}
