#include <bits/stdc++.h>
using namespace std;
const long long mx = 100000000000000000;
void dijkstra(int ss, vector<pair<int, int>> adj[], vector<int> &arr, vector<long long> &d)
{
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> q;
q.push({0, ss});
d[ss] = 0;
long long s, cd;
while (!q.empty())
{
s = q.top().second;
cd = q.top().first;
q.pop();
if (cd > d[s])
continue;
arr.push_back(s);
for (auto x : adj[s])
{
if (d[x.first] > d[s] + x.second)
{
d[x.first] = d[s] + x.second;
q.push({d[x.first], x.first});
}
}
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, ss, tt, u, v;
cin >> n >> m >> ss >> tt >> u >> v;
ss--, tt--, u--, v--;
int a, b, c;
vector<pair<int, int>> adj[n];
for (int i = 0; i < m; i++)
{
cin >> a >> b >> c;
adj[a - 1].push_back({b - 1, c});
adj[b - 1].push_back({a - 1, c});
}
long long vd, ud;
vector<long long> du(n, mx);
vector<long long> dv(n, mx);
vector<long long> dsum(n);
vector<long long> d(n, mx);
vector<int> brr;
vector<int> arr;
dijkstra(u, adj, brr, du);
dijkstra(v, adj, brr, dv);
dijkstra(ss, adj, arr, d);
for (int i = 0; i < n; i++)
{
dsum[i] = du[i] + dv[i];
}
long long ans = dsum[v];
for (auto i : arr)
{
vd = dv[i];
ud = du[i];
for (auto x : adj[i])
{
if (d[i] == d[x.first] + x.second)
{
du[i] = min(du[i], du[x.first]);
dv[i] = min(dv[i], dv[x.first]);
}
}
dsum[i] = min(du[i] + vd, dv[i] + ud);
for (auto x : adj[i])
{
if (d[i] == d[x.first] + x.second)
{
dsum[i] = min(dsum[i], dsum[x.first]);
}
}
}
ans = min(ans, dsum[tt]);
cout << ans << "\n";
return 0;
}
