#include <bits/stdc++.h>
using namespace std;
#define int int64_t
#define pii pair<int, int>
int dijsktra(int source, int dest, vector<set<pii>> &g) {
int n = g.size();
priority_queue<pii> pq;
vector<int> d(g.size(), 1e16);
d[source] = 0;
for (int i=0;i<g.size();i++) {
pq.push({-d[i], i});
}
vector<bool> proc(n, false);
while (!pq.empty()) {
pii p=pq.top();pq.pop();
if (proc[p.second]) continue;
proc[p.second] = true;
for (pii x : g[p.second]) {
if (d[p.second] + x.second < d[x.first]) {
d[x.first] = d[p.second] + x.second;
pq.push({-d[x.first], x.first});
}
}
}
return d[dest];
}
vector<int> dijsktra(int source, vector<set<pii>> &g) {
int n = g.size();
priority_queue<pii> pq;
vector<int> d(g.size(), 1e16);
d[source] = 0;
for (int i=0;i<g.size();i++) {
pq.push({-d[i], i});
}
vector<bool> proc(n, false);
while (!pq.empty()) {
pii p=pq.top();pq.pop();
if (proc[p.second]) continue;
proc[p.second] = true;
for (pii x : g[p.second]) {
if (d[p.second] + x.second < d[x.first]) {
d[x.first] = d[p.second] + x.second;
pq.push({-d[x.first], x.first});
}
}
}
return d;
}
signed main() {
// freopen("in.txt", "r", stdin);
int n, m;cin>>n>>m;
int s, t;cin>>s>>t;
int u, v;cin>>u>>v;
vector<set<pii>> g(n);
for (int i=0;i<m;i++) {
int a, b, c;cin>>a>>b>>c;
a--;b--;
g[a].insert({b, c});
g[b].insert({a, c});
}
s--;t--;u--;v--;
// dijsktra
vector<int> d = dijsktra(s, g);
vector<bool> proc(n, false);
queue<int> q;
q.push(t);
vector<set<pii>> cp = g;
// all edges going away from the sink
while (!q.empty()) {
int p=q.front();q.pop();
if (proc[p]) continue;
proc[p] = true;
set<pii> temp = g[p];
for (auto x : g[p]) {
if (d[p] == d[x.first] + x.second) {
// set edge weight to zero of node p
temp.erase(temp.find(x));
temp.insert({x.first, 0});
q.push(x.first);
}
}
g[p] = temp;
}
int val = dijsktra(u, v, g);
g.clear();
for (int i=0;i<n;i++) {
g.push_back(cp[i]);
}
q.push(t);
proc = vector<bool>(n, false);
while (!q.empty()) {
int p=q.front();q.pop();
if (proc[p]) continue;
proc[p] = true;
for (auto x : g[p]) {
if (d[p] == d[x.first] + x.second) {
// edges going towards the sink
g[x.first].erase(g[x.first].find({p, x.second}));
g[x.first].insert({p, 0});
q.push(x.first);
}
}
}
cout << min(dijsktra(u, v, g), val) << "\n";
}
