#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll, ll>
vector<pll> graph[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});
}
}
}
}
ll dfs(ll v, ll par)
{
if (wyn[par][v] < oo)
return wyn[par][v];
wyn[par][v] = dist[0][v];
for (auto u : graph[v])
{
if (dist[par + 2][v] + u.second + dist[(par ^ 1) + 2][u.first] == min_dist)
{
wyn[par][v] = min(wyn[par][v], dfs(u.first, par));
}
}
return wyn[par][v];
}
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];
fill(wyn[0], wyn[0] + n + 1, oo);
fill(wyn[1], wyn[1] + n + 1, oo);
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
init();
ll ans = dist[0][V];
for (ll i = 1; i <= n; i++)
{
if (dist[2][i] + dist[3][i] == min_dist)
ans = min(ans, min(dfs(i, 0), dfs(i, 1)) + dist[1][i]);
}
cout << ans << '\n';
}
