// Author: Ivan Teo
// Created: Sun Jul 28 10:10:07 2024
#define TASKNAME "joi"
#include <bits/stdc++.h>
using namespace std;
#define fore(i, a, b) for (int i = (a); i <= (b); i++)
#define ford(i, a, b) for (int i = (a); i >= (b); i--)
#define int long long
using vi = vector<int>;
using ii = pair<int, int>;
#define pb emplace_back
#define fi first
#define se second
#define sz(v) ((int)v.size())
#define all(v) v.begin() + 1, v.end()
#define alll(v) v.begin(), v.end()
#define db(x) cerr << "[" << #x << " = " << x << "]"
#define ell cerr << "\n=========================================\n"
#define el cerr << '\n'
#define Unique(v) v.erase(unique(alll(v)), v.end())
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int Rand(int l, int r)
{
assert(l <= r);
return uniform_int_distribution<int> (l, r)(rng);
}
template<int D, typename T> struct Vec : public vector < Vec < D - 1, T >>
{
template<typename... Args> Vec(int n = 0, Args... args) : vector < Vec < D - 1, T >> (n, Vec < D - 1, T > (args...)) {}
};
template<typename T> struct Vec<1, T> : public vector<T>
{
Vec(int n = 0, const T &val = T()) : vector<T>(n, val) {}
};
template<class T>void minimize(T &a, T b)
{
if(a > b)
{
a = b;
}
}
const int INF = 1e18;
const int N = 1e5 + 5;
vector<pair<int, int>>e[N];
void dijkstra(int vertex, vector<int> &d)
{
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>>pq;
pq.emplace(d[vertex] = 0, vertex);
bitset<N>vis;
while(!pq.empty())
{
auto [w, u] = pq.top();
pq.pop();
if(w == d[u])
{
for(auto& [v, edge_w] : e[u])
{
int W = w + edge_w;
if(W < d[v])
{
pq.emplace(d[v] = W, v);
}
}
}
}
}
void ivan()
{
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for(int i = 0; i < m; i++)
{
int a, b, c;
cin >> a >> b >> c;
e[a].emplace_back(b, c);
e[b].emplace_back(a, c);
}
vector<int>d_s(n + 1, INF), d_u(n + 1, INF), d_v(n + 1, INF), dp_u(n + 1, INF), dp_v(n + 1, INF);
dijkstra(s, d_s);
dijkstra(u, d_u);
dijkstra(v, d_v);
int ans = d_u[v];
function<void(int)>dfs;
dfs = [&] (int vertex)
{
if(dp_u[vertex] != INF)
{
return;
}
dp_u[vertex] = d_u[vertex];
dp_v[vertex] = d_v[vertex];
for(auto& [next_vertex, w] : e[vertex])
{
if(d_s[next_vertex] + w == d_s[vertex])
{
dfs(next_vertex);
minimize(dp_u[vertex], dp_u[next_vertex]);
minimize(dp_v[vertex], dp_v[next_vertex]);
}
}
minimize(ans, min(dp_v[vertex] + d_u[vertex], dp_u[vertex] + d_v[vertex]));
};
dfs(t);
cout << ans;
}
signed main()
{
cin.tie(0)->sync_with_stdio(0);
if (fopen(TASKNAME".inp", "r"))
{
freopen(TASKNAME".inp", "r", stdin);
freopen(TASKNAME".out", "w", stdout);
}
int tc = 1;
// cin >> tc;
while (tc--) ivan();
el, cerr << "Execution Time: " << 1.0 * clock() / CLOCKS_PER_SEC << "s", el;
return 0;
}
