#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN = 1e5 + 500;
const ll INF = 1e16;
int n, m;
int s,t,u,v;
vector<pair<int, ll> > susjedi[MAXN], parent[MAXN], dag[MAXN];
int bio[MAXN], bio2[MAXN];
queue<int> q;
ll distu[MAXN], distv[MAXN], dists[MAXN];
pair<ll, ll> dp[MAXN];
ll rj = INF;
set<pair<ll, ll> > sett;
void bfs (int x) {
for(int i = 0; i < n; i++){
if(i == s){
sett.insert(make_pair(0,s));
dists[s] = 0;
continue;
}
sett.insert(make_pair(INF,i));
dists[i] = INF;
}
while(!sett.empty()){
int x = (*sett.begin()).second;
sett.erase(sett.begin());
for (auto it: susjedi[x]) {
int nx = it.first;
if (dists[nx] > dists[x] + it.second) {
sett.erase({dists[nx], nx});
dists[nx] = dists[x] + it.second;
sett.insert ({dists[nx], nx});
parent[nx].clear ();
parent[nx].push_back ({x, it.second});
}
else if (dists[nx] == dists[x] + it.second) {
parent[nx].push_back ({x, it.second});
}
}
}
}
void dfs (int x) {
bio[x] = -2;
for (auto nx: parent[x]) {
dag[nx.first].push_back({x, nx.second});
if (bio[nx.first] != -2) dfs (nx.first);
}
}
void dijkstra(){
for(int i = 0; i < n; i++){
if(i == u){
sett.insert(make_pair(0,u));
distu[u] = 0;
continue;
}
sett.insert(make_pair(INF,i));
distu[i] = INF;
}
while(!sett.empty()){
int x = (*sett.begin()).second;
sett.erase(sett.begin());
for (auto it: susjedi[x]) {
int nx = it.first;
if (distu[nx] > distu[x] + it.second) {
sett.erase({distu[nx], nx});
distu[nx] = distu[x] + it.second;
sett.insert ({distu[nx], nx});
}
}
}
sett.clear ();
for(int i = 0; i < n; i++){
if(i == v){
sett.insert(make_pair(0,v));
distv[v] = 0;
continue;
}
sett.insert(make_pair(INF,i));
distv[i] = INF;
}
while(!sett.empty()){
int x = (*sett.begin()).second;
sett.erase(sett.begin());
for (auto it: susjedi[x]) {
int nx = it.first;
if (distv[nx] > distv[x] + it.second) {
sett.erase({distv[nx], nx});
distv[nx] = distv[x] + it.second;
sett.insert ({distv[nx], nx});
}
}
}
}
void solve () {
dijkstra ();
for (int i = 0; i < n; i++) {
if (bio[i] != -2) continue;
dp[i].first = distu[i];
dp[i].second = distv[i];
}
rj = distu[v];
memset (bio2, -1, sizeof (bio2));
q.push (s);
bio2[s] = 0;
while (!q.empty ()) {
int x = q.front ();
q.pop ();
for (auto nx: dag[x]) {
dp[nx.first].first = min (dp[nx.first].first, dp[x].first);
// cout << "AAAAAA " << x << ' ' << nx.first << ' ' << dp[nx.first].first << ' ' << dp[nx.first].second << "\n";
if (bio2[nx.first] == -1) {
bio2[nx.first] = bio2[x] + 1;
q.push (nx.first);
}
}
}
memset (bio2, -1, sizeof (bio2));
q.push (t);
bio2[t] = 0;
while (!q.empty ()) {
int x = q.front ();
q.pop ();
for (auto nx: parent[x]) {
dp[nx.first].second = min (dp[nx.first].second, dp[x].second);
// cout << "AAAAAAAAAAAA" << ' ' << x << ' ' << dp[x].second << ' ' << nx.first << ' ' << dp[nx.first].second << "\n";
if (bio2[nx.first] == -1) {
bio2[nx.first] = bio2[x] + 1;
q.push (nx.first);
}
}
}
for (int i = 0; i < n; i++) {
if (bio[i] != -2) continue;
rj = min (rj, dp[i].first + dp[i].second);
dp[i].first = distu[i];
dp[i].second = distv[i];
}
memset (bio2, -1, sizeof (bio2));
q.push (s);
bio2[s] = 0;
while (!q.empty ()) {
int x = q.front ();
q.pop ();
for (auto nx: dag[x]) {
dp[nx.first].second = min (dp[nx.first].second, dp[x].second);
// cout << "AAAAAA " << x << ' ' << nx.first << ' ' << dp[nx.first].first << ' ' << dp[nx.first].second << "\n";
if (bio2[nx.first] == -1) {
bio2[nx.first] = bio2[x] + 1;
q.push (nx.first);
}
}
}
memset (bio2, -1, sizeof (bio2));
q.push (t);
bio2[t] = 0;
while (!q.empty ()) {
int x = q.front ();
q.pop ();
for (auto nx: parent[x]) {
dp[nx.first].first = min (dp[nx.first].first, dp[x].first);
// cout << "AAAAAAAAAAAA" << ' ' << x << ' ' << dp[x].second << ' ' << nx.first << ' ' << dp[nx.first].second << "\n";
if (bio2[nx.first] == -1) {
bio2[nx.first] = bio2[x] + 1;
q.push (nx.first);
}
}
}
for (int i = 0; i < n; i++) {
if (bio[i] != -2) continue;
rj = min (rj, dp[i].first + dp[i].second);
}
}
int main () {
ios_base::sync_with_stdio (false);
cin.tie (0);
memset (bio, -1, sizeof (bio));
cin >> n >> m >> s >> t >> u >> v;
s--;t--;u--;v--;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
a--;b--;
susjedi[a].push_back ({b, c});
susjedi[b].push_back ({a, c});
}
bfs (s);
dfs (t);
solve ();
cout << rj;
return 0;
}
