#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll, ll>
vector<pll> graph[100003];
vector<ll> dag[2][100003];
ll deg[2][100003];
ll n, m, S, T, U, V, oo = 1e18 + 1, min_dist;
ll dist[4][100003];
ll wyn[2][100003];
void Dijkstra(ll st, ll par)
{
fill(dist[par], dist[par] + n + 1, oo);
dist[par][st] = 0;
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({0, st});
while (pq.size())
{
auto [d, v] = pq.top();
pq.pop();
if (d != dist[par][v])
continue;
for (auto [u, w] : graph[v])
{
if (d + w < dist[par][u])
{
dist[par][u] = d + w;
pq.push({d + w, u});
}
}
}
}
void init()
{
cin >> n >> m >> S >> T >> U >> V;
ll a, b, c;
for (ll i = 1; i <= m; i++)
{
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
Dijkstra(U, 0);
Dijkstra(V, 1);
Dijkstra(S, 2);
Dijkstra(T, 3);
min_dist = dist[2][T];
}
void construct()
{
for (ll v = 1; v <= n; v++)
{
for (auto [u, w] : graph[v])
{
if ((dist[2][v] + w + dist[3][u]) == min_dist)
{
dag[0][v].push_back(u);
deg[0][u]++;
dag[1][u].push_back(v);
deg[1][v]++;
}
}
}
}
void topo_sort(ll typ){
stack<ll> kol;
queue<ll> q;
for (ll i = 1; i <= n; i++)
{
if (!deg[typ][i])
q.push(i);
}
while(q.size())
{
ll v = q.front();
q.pop();
kol.push(v);
for (ll u : dag[typ][v])
{
deg[typ][u]--;
if (!deg[typ][u])
q.push(u);
}
}
while(kol.size())
{
ll v = kol.top();
kol.pop();
wyn[typ][v] = dist[0][v];
for (auto u : dag[typ][v])
wyn[typ][v] = min(wyn[typ][v], wyn[typ][u]);
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
init();
ll ans = dist[0][V];
construct();
topo_sort(0);
topo_sort(1);
for (ll i = 1; i <= n; i++)
{
if (dist[2][i] + dist[3][i] == min_dist)
ans = min(ans, min(wyn[0][i], wyn[1][i]) + dist[1][i]);
}
cout << ans << '\n';
}
