#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int MAXN = 4e5 + 10;
const ll INF = 1e18;
ll dist[MAXN][3];
int marc[MAXN][3];
int n, m;
vector<pair<int, int>> adj[MAXN];
void dijkstra(int v, int x){
priority_queue<pair<ll, int>> q;
for(int i=1; i<=4*n; i++) dist[i][x] = INF;
dist[v][x] = 0; q.push({0, v});
while(!q.empty()){
auto [d, v] = q.top(); q.pop();
if(marc[v][x]) continue;
marc[v][x] = 1;
for(auto [u, w] : adj[v]){
if(dist[v][x] + w < dist[u][x]){
dist[u][x] = dist[v][x] + w;
q.push({-dist[u][x], u});
}
}
}
}
int main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
vector<pair<int, pair<int, int>>> edges;
for(int i=1; i<=m; i++){
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
edges.push_back({a, {b, c}});
edges.push_back({b, {a, c}});
}
dijkstra(s, 0);
dijkstra(t, 1);
for(auto e : edges){
int x = e.first, y = e.second.first, w = e.second.second;
adj[x + 3 * n].push_back({y + 3 * n, w});
if(dist[x][0] + dist[x][1] == dist[t][0]){
adj[x + n].push_back({y + 3 * n, w});
adj[x + 2 * n].push_back({y + 3 * n, w});
}
if(dist[y][0] + dist[y][1] == dist[t][0]){
adj[x].push_back({y + n, w});
adj[x].push_back({y + 2 * n, w});
}
if(dist[x][0] + w + dist[y][1] == dist[t][0]) adj[x + n].push_back({y + n, 0});
if(dist[x][1] + w + dist[y][0] == dist[s][1]) adj[x + 2 * n].push_back({y + 2 * n, 0});
}
if(dist[u][0] + dist[u][1] == dist[t][0]){
adj[u].push_back({u + n, 0});
adj[u].push_back({u + 2 * n, 0});
}
dijkstra(u, 2);
cout << min({dist[v][2], dist[v + n][2], dist[v + 2 * n][2], dist[v + 3 * n][2]}) << "\n";
return 0;
}
