// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
#include <bits/stdc++.h>
using namespace std;
#define int ll
#define MAX LLONG_MAX
#define st first
#define nd second
#define endl '\n'
#define SZ(x) ((int)x.size())
#define ALL(x) x.begin(), x.end()
typedef long long ll;
typedef pair< int, int > ii;
typedef pair< int, ii > iii;
typedef vector< int > vi;
typedef vector< ii > vii;
typedef vector< iii > viii;
typedef vector< vi > vvi;
typedef vector< vii > vvii;
typedef vector< viii > vviii;
const int N = 1e5 + 5;
int n, m;
vii adj[N];
int um[N], vm[N];
vi flood(int s){
vi dis(n + 1, LLONG_MAX);
dis[s] = 0;
priority_queue<ii, vii, greater<ii>> q;
q.push({0, s});
while(q.size()){
auto [len, u] = q.top(); q.pop();
if(dis[u] != len) continue;
for(auto [v, w]: adj[u]){
if(dis[v] > dis[u] + w){
dis[v] = dis[u] + w;
q.push({dis[v], v});
}
}
}
return dis;
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
while(m--){
int x, y, z; cin >> x >> y >> z;
adj[x].push_back({y, z});
adj[y].push_back({x, z});
}
auto S = flood(s), T = flood(t), U = flood(u), V = flood(v);
vii dag;
for(int i=1; i<=n; i++){
if(S[i] + T[i] != S[t]) continue;
dag.push_back({T[i], i});
}
sort(ALL(dag));
int ans = U[v];
for(auto [len, x]: dag){
um[x] = U[x];
vm[x] = V[x];
for(auto [y, z]: adj[x]){
if(T[y] + z == len){
um[x] = min(um[x], um[y]);
vm[x] = min(vm[x], vm[y]);
}
}
ans = min(ans, um[x] + V[x]);
ans = min(ans, vm[x] + U[x]);
}
cout << ans;
}
