#include <bits/stdc++.h>
using namespace std;
/*
John Watson
https://codeforces.com/profile/quangminh98
Mua Code nhu mua Florentino !!
*/
#define faster() ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long
const ll oo = 1e18;
const int maxn = 1e5 + 9;
struct Near
{
int tar, id;
ll w;
Near(int tar, int id, ll w) : tar(tar), id(id), w(w) {}
};
vector<Near> adj[maxn];
int state[2 * maxn];
vector<vector<ll>> floyd(500, vector<ll>(500, oo));
int n, m, s, t, u, v;
void dijkstra2(int s)
{
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
vector<ll> dist(n + 2, oo);
pq.push({dist[s] = 0, s});
while (!pq.empty())
{
int u = pq.top().second;
ll w = pq.top().first;
pq.pop();
if (dist[u] != w) continue;
for (Near nxt : adj[u])
{
int v = nxt.tar;
int id = nxt.id;
ll ww = nxt.w;
if (dist[v] > dist[u] + (state[id] == 1 ? 0 : ww))
pq.push({dist[v] = dist[u] + (state[id] == 1 ? 0 : ww), v});
}
}
cout << dist[v] << '\n';
}
void dijkstra1(int s)
{
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
vector<pair<int, int>> prev(n + 2, {0, 0});
vector<ll> dist(n + 2, oo);
pq.push({dist[s] = 0, s});
while (!pq.empty())
{
int u = pq.top().second;
ll w = pq.top().first;
pq.pop();
if (dist[u] != w) continue;
for (Near nxt : adj[u])
{
int v = nxt.tar;
ll ww = nxt.w;
int id = nxt.id;
if (dist[v] > dist[u] + ww)
{
prev[v] = {u, id};
pq.push({dist[v] = dist[u] + ww, v});
}
}
}
while (t != s)
{
state[prev[t].second] = 1;
t = prev[t].first;
}
}
vector<ll> shortestPath(int s)
{
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
vector<ll> dist(n + 5, oo);
pq.push({dist[s] = 0, s});
while (!pq.empty())
{
int u = pq.top().second;
ll w = pq.top().first;
pq.pop();
if (dist[u] != w) continue;
for (Near nxt : adj[u])
{
int v = nxt.tar;
ll ww = nxt.w;
if (dist[v] > dist[u] + ww)
pq.push({dist[v] = dist[u] + ww, v});
}
}
return dist;
}
void solve_1()
{
vector<ll> froms = shortestPath(s), fromt = shortestPath(t), fromv = shortestPath(v);
ll ans = froms[v];
for (int vertex = 1; vertex <= n; vertex++)
if (froms[vertex] + fromt[vertex] == froms[t])
ans = min(ans, fromv[vertex]);
cout << ans << '\n';
}
void solve_3()
{
for (int i = 1; i <= n; i++) floyd[i][i] = 0;
for (int k = 1; k <= n; k++)
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
floyd[i][j] = min(floyd[i][j], floyd[i][k] + floyd[k][j]);
ll ans = floyd[u][v];
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
if (floyd[s][i] + floyd[i][j] + floyd[j][t] == floyd[s][t])
ans = min(ans, floyd[u][i] + floyd[j][v]);
cout << ans << '\n';
}
signed main()
{
if (fopen("test.inp", "r"))
{
freopen("test.inp", "r", stdin);
freopen("test.out", "w", stdout);
}
faster();
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; i++)
{
int u, v; cin >> u >> v;
ll w; cin >> w;
adj[u].emplace_back(v, i, w);
adj[v].emplace_back(u, i, w);
floyd[u][v] = floyd[v][u] = min(floyd[u][v], w);
}
if (s == u)
{
solve_1();
return 0;
}
if (n <= 300)
{
solve_3();
return 0;
}
dijkstra1(s);
dijkstra2(u);
return 0;
}
