#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
ll N, M, S, T, U, V;
vector<vector<pll>> graph;
vector<ll> lider;
vector<ll> siz;
stack<pll> changes;
vector<vector<ll>> dag;
const ll oo = 1e18;
ll Find(ll v)
{
if (lider[v] == v)
return v;
changes.push({v, lider[v]});
return lider[v] = Find(lider[v]);
}
void Union(ll a, ll b)
{
a = Find(a);
b = Find(b);
if (a == b)
return;
if (siz[a] < siz[b])
swap(a, b);
changes.push({b, b});
lider[b] = a;
siz[a] += siz[b];
}
void Rollback()
{
auto [v, p] = changes.top();
changes.pop();
if (v == p)
siz[lider[v]] -= siz[v];
lider[v] = p;
}
vector<ll> Dijkstra(ll st)
{
priority_queue<pll, vector<pll>, greater<pll>> pq;
vector<ll> dist(N + 1, oo);
dist[st] = 0;
pq.push({0, st});
while (pq.size())
{
auto [d, v] = pq.top();
pq.pop();
if (d != dist[v])
continue;
for (auto [u, c] : graph[v])
{
if (Find(v) == Find(u))
c = 0;
if (d + c < dist[u])
{
dist[u] = d + c;
pq.push({dist[u], u});
}
}
}
return dist;
}
void init()
{
cin >> N >> M >> S >> T >> U >> V;
graph.resize(N + 1);
dag.resize(N + 1);
siz.resize(N + 1, 1);
lider.resize(N + 1);
iota(lider.begin(), lider.end(), 0);
for (ll i = 1, a, b, c; i <= M; i++)
{
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
}
ll ans = oo;
void dfs(ll v)
{
ll t = changes.size();
if (v == T)
ans = min(ans, Dijkstra(U)[V]);
for (auto u : dag[v])
{
Union(v, u);
dfs(u);
while ((ll)changes.size() > t)
Rollback();
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
init();
vector<ll> dist = Dijkstra(S);
for (ll v = 1; v <= N; v++)
{
for (auto [u, c] : graph[v])
{
if (dist[v] + c == dist[u])
dag[v].push_back(u);
}
}
dfs(S);
cout << ans << '\n';
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
*/
