#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
const bool typetest = 0;
const int N = 1e5 + 5;
const ll Inf = 1e17;
int n, m, s, t, u, v, id[N];
vector<pair<int, ll>> adj[N];
ll d[4][N], dp[N][3];
void Read()
{
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; ++i)
{
int x, y, w;
cin >> x >> y >> w;
adj[x].push_back({y, w});
adj[y].push_back({x, w});
}
}
void Dijkstra(int x, ll d[N])
{
fill_n(d, N, Inf);
d[x] = 0;
struct Tque
{
int v;
ll w;
Tque(const int &v, const ll &w) : v(v), w(w)
{
}
bool operator<(const Tque &a) const
{
return w > a.w;
}
};
priority_queue<Tque> s;
s.push({x, 0});
while (s.size())
{
Tque c = s.top();
s.pop();
if (d[c.v] != c.w)
continue;
for (auto i : adj[c.v])
if (d[i.first] > c.w + i.second)
{
d[i.first] = c.w + i.second;
s.push({i.first, d[i.first]});
}
}
}
void Solve()
{
Dijkstra(s, d[1]);
Dijkstra(u, d[2]);
Dijkstra(v, d[3]);
for (int i = 1; i <= n; ++i)
id[i] = i;
sort(id + 1, id + n + 1, [&](const int &x, const int &y) {
return d[1][x] < d[1][y];
});
fill_n(&dp[0][0], N * 3, Inf);
for (int i = 1; i <= n; ++i)
{
dp[id[i]][0] = d[2][id[i]];
dp[id[i]][1] = d[3][id[i]];
for (auto j : adj[id[i]])
if (d[1][j.first] + j.second == d[1][id[i]])
{
dp[id[i]][0] = min(dp[j.first][0], dp[id[i]][0]);
dp[id[i]][1] = min(dp[j.first][1], dp[id[i]][1]);
dp[id[i]][2] = min(dp[j.first][2], dp[id[i]][2]);
}
dp[id[i]][2] = min(dp[id[i]][2], min(dp[id[i]][0] + d[3][id[i]], dp[id[i]][1] + d[2][id[i]]));
}
cout << min(dp[t][2], d[2][v]);
}
int32_t main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t(1);
if (typetest)
cin >> t;
for (int _ = 1; _ <= t; ++_)
{
Read();
Solve();
}
}
