#include <bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define Jungle "JOI18_commuter_pass"
#define getbit(x, i) (((x) >> (i)) & 1)
#define cntbit(x) __builtin_popcount(x)
#define _(x) ((x) & -(x))
#define MASK(x) (1 << (x))
#define MULTEST \
int nq; \
cin >> nq; \
while (nq--)
template <typename T>
void chkmin(T &a, T b)
{
if (a > b)
a = b;
}
template <typename T>
void chkmax(T &a, T b)
{
if (a < b)
a = b;
}
const int mod = 1e9 + 7;
int add(int x, int y)
{
return (1ll * x + y) % mod;
}
int sub(int x, int y)
{
return (1ll * x - y + mod) % mod;
}
int mul(int x, int y)
{
return 1ll * x * y % mod;
}
void read(int &x)
{
x = 0;
int c = 0;
while ((c = getchar()) && (c > '9' || c < '0'))
;
for (; c >= '0' && c <= '9'; c = getchar())
x = x * 10 + c - '0';
}
const int maxn = 1e5;
int n, m, S, T, U, V;
vector<tuple<int, int, int>> edges;
vector<pair<int, int>> undirected_graph[maxn + 2];
void init(void)
{
read(n);
read(m);
read(S);
read(T);
read(U);
read(V);
for (int i = 1; i <= m; i++)
{
int u, v, w;
read(u);
read(v);
read(w);
edges.push_back({u, v, w});
undirected_graph[u].push_back({v, w});
undirected_graph[v].push_back({u, w});
}
}
const long long inf = 2e18;
void Dijkstra(const int source, long long dist[maxn + 2])
{
for (int i = 1; i <= n; i++)
dist[i] = inf;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> store;
store.push({dist[source] = 0, source});
while (store.size())
{
const auto [d, u] = store.top();
store.pop();
if (dist[u] != d)
continue;
for (const auto [v, w] : undirected_graph[u])
if (dist[v] > d + w)
store.push({dist[v] = d + w, v});
}
}
queue<int> q;
int indeg[maxn + 2];
vector<int> DAG[maxn + 2], topo;
long long dist[3][maxn + 2], dpU[maxn + 2], dpV[maxn + 2], dp[maxn + 2];
void solve(void)
{
init();
Dijkstra(S, dist[0]);
Dijkstra(U, dist[1]);
Dijkstra(V, dist[2]);
for (const auto &[u, v, w] : edges)
{
if (dist[0][u] + w == dist[0][v])
{
DAG[u].push_back(v);
++indeg[v];
}
if (dist[0][v] + w == dist[0][u])
{
DAG[v].push_back(u);
++indeg[u];
}
}
q.push(S);
while (q.size())
{
const int u = q.front();
q.pop();
topo.push_back(u);
for (const int v : DAG[u])
if (--indeg[v] == 0)
q.push(v);
}
for (int i = 1; i <= n; i++)
dpU[i] = dpV[i] = dp[i] = inf;
dpU[S] = dist[1][S];
dpV[S] = dist[2][S];
dp[S] = dpU[S] + dpV[S];
for (const int &u : topo)
{
chkmin(dp[u], min(dpU[u] + dist[2][u], dpV[u] + dist[1][u]));
for (const int &v : DAG[u])
{
chkmin(dp[v], dp[u]);
chkmin(dpU[v], min(dpU[u], dist[1][v]));
chkmin(dpV[v], min(dpV[u], dist[2][v]));
}
}
cout << min(dp[T], dist[1][V]);
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(nullptr);
cout.tie(nullptr);
if (fopen(Jungle ".inp", "r"))
{
freopen(Jungle ".inp", "r", stdin);
freopen(Jungle ".out", "w", stdout);
}
// MULTEST
solve();
// cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
