#include <bits/stdc++.h>
#ifdef DEBUG
#include "../templates/debug.h"
#else
#define deb(x...)
#endif
using namespace std;
#define int long long
signed main() {
iostream::sync_with_stdio(false);
cin.tie(nullptr);cout.tie(nullptr);
int n, m;cin >> n >> m;
int s, t;cin >> s >> t; --s;--t;
int u, v;cin >> u >> v; --u;--v;
vector<array<int, 3>> fake_edg(m);
vector<vector<pair<int, int>>> fake_adj(n);
for(auto &[a, b, c] : fake_edg){
cin >> a >> b >> c;
--a;--b;
fake_adj[a].push_back({b, c});
fake_adj[b].push_back({a, c});
}
set<pair<int,int>> selected_edges;/*{{{*/
priority_queue<pair<int,int>> pq;
vector<int> fake_dist(n, 1e18);
fake_dist[s] = 0;
pq.push({-fake_dist[s], s});
while(!pq.empty()){
auto [dd, x] = pq.top();
dd = -dd;
pq.pop();
if(fake_dist[x] != dd)continue;
for(auto [e, w] : fake_adj[x]){
if(fake_dist[e] > fake_dist[x] + w){
fake_dist[e] = fake_dist[x] + w;
pq.push({-fake_dist[e], e});
}
}
}
vector<vector<int>> temp_adj(n);
vector<bool> visited(n, false);
queue<int> q;
q.push(s);
visited[s] = true;
while(!q.empty()){
int x = q.front();
q.pop();
for(auto [e, w] : fake_adj[x]){
if(fake_dist[e] == fake_dist[x] + w){
temp_adj[e].push_back(x);
if(!visited[e]){
visited[e] = true;
q.push(e);
}
}
}
}
deb(temp_adj);
fill(visited.begin(), visited.end(), false);
q.push(t);
visited[t] = true;
while(!q.empty()){
int x = q.front();
q.pop();
for(int e : temp_adj[x]){
selected_edges.insert({min(e, x), max(e, x)});
if(!visited[e]){
visited[e] = true;
q.push(e);
}
}
}
deb(selected_edges);
vector<vector<pair<int,int>>> adj(n);
for(auto [a, b, c] : fake_edg){
if(a > b)swap(a, b);
if(selected_edges.find({a, b}) != selected_edges.end()){
if(fake_dist[a] < fake_dist[b]){
deb(a, b);
adj[a].push_back({b, 0});
adj[b].push_back({a, c});
}
else{
deb(b, a);
adj[b].push_back({a, 0});
adj[a].push_back({b, c});
}
}
else{
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
}
deb(adj);
vector<int> dist(n, 1e18);
dist[u] = 0;
pq.push({-dist[u], u});
while(!pq.empty()){
auto [dd, x] = pq.top();
pq.pop();
dd = -dd;
if(dist[x] != dd)continue;
for(auto [e, w] : adj[x]){
if(dist[e] > dist[x] + w){
dist[e] = dist[x] + w;
pq.push({-dist[e], e});
}
}
}
int ans = dist[v];
adj.clear();
adj.resize(n);
for(auto [a, b, c] : fake_edg){/*{{{*/
if(a > b)swap(a, b);
if(selected_edges.find({a, b}) != selected_edges.end()){
if(fake_dist[a] > fake_dist[b]){
deb(a, b);
adj[a].push_back({b, 0});
adj[b].push_back({a, c});
}
else{
deb(b, a);
adj[b].push_back({a, 0});
adj[a].push_back({b, c});
}
}
else{
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
}
fill(dist.begin(), dist.end(), 1e18);
dist[u] = 0;
pq.push({-dist[u], u});
while(!pq.empty()){
auto [dd, x] = pq.top();
pq.pop();
dd = -dd;
if(dist[x] != dd)continue;
for(auto [e, w] : adj[x]){
if(dist[e] > dist[x] + w){
dist[e] = dist[x] + w;
pq.push({-dist[e], e});
}
}
}
ans = min(ans, dist[v]);
cout << ans << "\n";/*}}}*//*}}}*/
}
