#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
#define FOR(i , a , b) for(int i = (a) , _b = (b); i <= _b; ++i)
#define BIT(mask , x) (((mask) >> (x)) & (1))
#define MASK(x) ((LL)(1)<<(x))
#define sz(x) (int)(x).size()
#define Time_used cerr << "\n Time lapsed : " << 1.0 * clock() / CLOCKS_PER_SEC << " s\n";
template<class T1 , class T2>
bool maximize(T1 &a , T2 b){
if (a < b) return a = b , true; else return false;
}
template<class T1 , class T2>
bool minimize(T1 &a , T2 b){
if (a > b) return a = b , true; else return false;
}
template<class T>
void compress(vector<T>&data){
sort(data.begin() , data.end());
data.resize(unique(data.begin() , data.end()) - data.begin());
}
template<class T1 , class T2>
T2 Find(const vector<T1>&data , T2 y){
return upper_bound(data.begin() , data.end() , y) - data.begin();
}
const int N = (int) 1e5;
const int M = (int) 2e5;
const LL inf = (LL)1e18;
int x[M + 2] , y[M + 2] , c[M + 2];
int n , m;
int source , sink , n_source , n_sink;
namespace subtask1{
bool check(){
return n <= 300;
}
const int maxn = 300;
LL f[maxn + 2][maxn + 2];
void main_code(){
memset(f,0x3f,sizeof f);
for(int i = 1; i <= n; ++i) f[i][i] = 0;
for(int i = 1; i <= m; ++i){
minimize(f[x[i]][y[i]] , c[i]);
minimize(f[y[i]][x[i]] , c[i]);
}
for(int k = 1; k <= n; ++k){
for(int i = 1; i <= n; ++i) {
for(int j = 1; j <= n; ++j) {
minimize(f[i][j] , f[i][k] + f[k][j]);
}
}
}
LL min_dist = f[source][sink];
LL ans = f[n_source][n_sink];
for(int i = 1; i <= n; ++i){
for(int j = 1; j <= n; ++j){
if (f[source][i] + f[i][j] + f[j][sink] == min_dist){
minimize(ans , f[n_source][i] + f[j][n_sink]);
minimize(ans , f[n_sink][i] + f[j][n_source]);
}
}
}
cout << ans << '\n';
return;
}
}
namespace subtask2{
bool check(){
return true;
}
vector<int> ke[N + 2];
void add_canh(int u , int v , int id){
ke[u].push_back(id) , ke[v].push_back(id);
return;
}
void build_djisktra(int source , LL d[]){
for(int i = 1; i <= n; ++i) d[i] = inf;
priority_queue<pair<LL,int> , vector<pair<LL,int>> , greater<pair<LL,int>>> pq;
d[source] = 0;
pq.push({d[source] , source});
while (pq.size()){
int u = pq.top().second;
LL cost = pq.top().first;
pq.pop();
if (cost != d[u]) continue;
for(int id : ke[u]){
int v = x[id] ^ y[id] ^ u;
if (minimize(d[v] , cost + c[id])){
pq.push({d[v] , v});
}
}
}
return;
}
LL tmp[N + 2] = {} , d[N + 2] = {} , rev_dist[N + 2] = {};
LL process(int source , int sink){
build_djisktra(source , d);
build_djisktra(sink , rev_dist);
LL min_dist = d[sink];
for(int i = 1; i <= n; ++i) tmp[i] = inf;
priority_queue<pair<LL,int>,vector<pair<LL,int>>,greater<pair<LL,int>>>pq;
tmp[n_source] = 0;
pq.push({tmp[n_source] , n_source});
while (sz(pq)){
int u = pq.top().second;
LL cost = pq.top().first;
pq.pop();
if (cost != tmp[u]) continue;
for(int id : ke[u]){
int v = u ^ x[id] ^ y[id];
LL cost_change = (d[u] + rev_dist[v] + c[id] == min_dist ? 0 : c[id]);
if (minimize(tmp[v] , cost + cost_change)) pq.push({tmp[v] , v});
}
}
return tmp[n_sink];
}
void main_code(){
for(int i = 1; i <= m; ++i) add_canh(x[i] , y[i] , i);
cout << min(process(source , sink) , process(sink , source));
return ;
}
}
int main(){
ios :: sync_with_stdio(false);
cin.tie(0) ; cout.tie(0) ;
#define name "main"
if (fopen(name".inp","r")){
freopen(name".inp","r",stdin);
freopen(name".out","w",stdout);
}
cin >> n >> m;
cin >> source >> sink;
cin >> n_source >> n_sink;
for(int i = 1; i <= m; ++i) cin >> x[i] >> y[i] >> c[i];
if (subtask1::check()) return subtask1::main_code() , 0;
if (subtask2::check()) return subtask2::main_code() , 0;
return 0;
}
