#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
using namespace std;
using ll = long long;
vector<vector<int>> lstadj(1e5 + 1, vector<int>(0));
vector<int> topsort(0);
vector<bool> vis(1e5 + 1, false);
void dfs(int node)
{
vis[node] = true;
for (int nxt : lstadj[node]) if (!vis[nxt]) dfs(nxt);
topsort.push_back(node);
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector<vector<pair<ll, int>>> adj(n + 1, vector<pair<ll, int>>(0));
while (m--)
{
int a, b;
ll c;
cin >> a >> b >> c;
adj[a].push_back({ c, b }), adj[b].push_back({ c, a });
}
priority_queue<pair<ll, int>> udjk;
vector<ll> du(n + 1, -1);
udjk.push({ 0, u });
while (!udjk.empty())
{
ll d = -udjk.top().first;
int node = udjk.top().second;
udjk.pop();
if (du[node] == -1)
{
du[node] = d;
for (pair<ll, int> nxt : adj[node]) udjk.push({ -d - nxt.first, nxt.second });
}
}
vector<ll> dv(n + 1, -1);
priority_queue<pair<ll, int>> vdjk;
vdjk.push({ 0, v });
while (!vdjk.empty())
{
ll d = -vdjk.top().first;
int node = vdjk.top().second;
vdjk.pop();
if (dv[node] == -1)
{
dv[node] = d;
for (pair<ll, int> nxt : adj[node]) vdjk.push({ -d - nxt.first, nxt.second });
}
}
vector<ll> ds(n + 1, -1);
priority_queue<pair<ll, pair<int, int>>> sdjk;
sdjk.push({ 0, {s, 0} });
while (!sdjk.empty())
{
ll d = -sdjk.top().first;
int node = sdjk.top().second.first, lst = sdjk.top().second.second;
sdjk.pop();
if (d == ds[node]) lstadj[node].push_back(lst);
else if (ds[node] == -1)
{
ds[node] = d;
if (lst > 0) lstadj[node].push_back(lst);
for (pair<ll, int> nxt : adj[node]) sdjk.push({ -d - nxt.first, {nxt.second, node} });
}
}
dfs(t);
vector<int> dtopsort = topsort;
vector<ll> ddu = du, ddv = dv;
while (!topsort.empty())
{
int node = topsort.back();
for (int nxt : lstadj[node]) if (vis[nxt]) if (dv[node] < dv[nxt]) dv[nxt] = dv[node];
topsort.pop_back();
}
ll ans = du[n] + dv[n];
for (int i = 1; i < n; i++) if (du[i] + dv[i] < ans) ans = du[i] + dv[i];
while (!dtopsort.empty())
{
int node = dtopsort.back();
for (int nxt : lstadj[node]) if (vis[nxt]) if (ddu[node] < ddu[nxt]) ddu[nxt] = ddu[node];
dtopsort.pop_back();
}
for (int i = 1; i < n; i++) if (ddu[i] + ddv[i] < ans) ans = ddu[i] + ddv[i];
cout << ans;
}
