#include <bits/stdc++.h>
using namespace std;
using ll = long long;
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
int main(){
int n,m,s,t,u,v;
cin >> n >> m >> s >> t >> u >> v,s--,t--,u--,v--;
vector<vector<int>> g(n);
vector<tuple<int,int,int>> e;
for(int i = 0; i < m; i++){
int a,b,c;
cin >> a >> b >> c,a--,b--;
g[a].push_back(i);
g[b].push_back(i);
e.emplace_back(a,b,c);
}
auto f = [&](int i,int x){
return x ^ get<0>(e[i]) ^ get<1>(e[i]);
};
vector<ll> dist(n,1e17);
vector<vector<int>> par(n);
priority_queue<pair<ll,int>> pq;
dist[s] = 0;
pq.emplace(0,s);
while(pq.size()){
auto [dst,cur] = pq.top(); pq.pop();
if(-dst > dist[cur]) continue;
for(int id: g[cur]){
int nxt = f(id,cur);
ll nw = dist[cur] + get<2>(e[id]);
if(nw < dist[nxt]){
dist[nxt] = nw;
pq.emplace(-nw,nxt);
par[nxt].clear();
par[nxt].push_back(id);
}else if(nw == dist[nxt]){
par[nxt].push_back(id);
}
}
}
stack<int> stk;
stk.push(t);
vector<int> vis(n);
while(stk.size()){
int cur = stk.top(); stk.pop();
for(int id: par[cur]){
get<2>(e[id]) = 0;
if(!vis[f(id,cur)]){
stk.push(f(id,cur));
vis[f(id,cur)] = 1;
}
}
}
dist = vector<ll>(n,1e17);
dist[u] = 0;
pq.emplace(0,u);
while(pq.size()){
auto [dst,cur] = pq.top(); pq.pop();
if(-dst > dist[cur]) continue;
for(int id: g[cur]){
int nxt = f(id,cur);
ll nw = dist[cur] + get<2>(e[id]);
if(nw < dist[nxt]){
dist[nxt] = nw;
pq.emplace(-nw,nxt);
}
}
}
cout << dist[v];
}
