/******************************************************************************
Welcome to GDB Online.
GDB online is an online compiler and debugger tool for C, C++, Python, Java, PHP, Ruby, Perl,
C#, OCaml, VB, Swift, Pascal, Fortran, Haskell, Objective-C, Assembly, HTML, CSS, JS, SQLite, Prolog.
Code, Compile, Run and Debug online from anywhere in world.
*******************************************************************************/
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
const int N = 1e5 + 5;
long long int n, m, s, t, u, v;
long long int a, b, c;
vector<pair<long long int, long long int>> edge[N];
long long int du[N], dus[N];
long long int dv[N], dvs[N];
long long int ds[N];
vector<long long int> par[N];
bool visited[N];
long long int pathU(long long int cur){
if(visited[cur]){
return dus[cur];
}
visited[cur] = true;
for(int i = 0; i < par[cur].size(); i++){
dus[cur] = min(dus[cur], pathU(par[cur][i]));
}
return dus[cur];
}
long long int pathV(long long int cur){
if(visited[cur]){
return dvs[cur];
}
visited[cur] = true;
for(int i = 0; i < par[cur].size(); i++){
dvs[cur] = min(dvs[cur], pathV(par[cur][i]));
}
return dvs[cur];
}
void solve(){
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for(int i = 0; i < m; i++){
cin >> a >> b >> c;
edge[a].push_back({b, c});
edge[b].push_back({a, c});
}
for(int i = 0; i < N; i++){
du[i] = dv[i] = ds[i] = 1e9*(n + 1);
}
priority_queue<pair<long long int, long long int>, vector<pair<long long int, long long int>>, greater<pair<long long int, long long int>>> pq;
//djikstra dari u
pq.push({0, u});
while(!pq.empty()){
long long int cst = pq.top().fi, cur = pq.top().se;
pq.pop();
if(du[cur] > cst){
du[cur] = cst;
for(int i = 0; i < edge[cur].size(); i++){
pq.push({edge[cur][i].se + cst, edge[cur][i].fi});
}
}
}
//djikstra dari v
pq.push({0, v});
while(!pq.empty()){
long long int cst = pq.top().fi, cur = pq.top().se;
pq.pop();
if(dv[cur] > cst){
dv[cur] = cst;
for(int i = 0; i < edge[cur].size(); i++){
pq.push({edge[cur][i].se + cst, edge[cur][i].fi});
}
}
}
//cari shortest path
vector<long long int> parTem[N];
pq.push({0, s});
while(!pq.empty()){
long long int cur = pq.top().se, cst = pq.top().fi;
pq.pop();
if(cur == t){
break;
}
if(ds[cur] >= cst){
ds[cur] = cst;
for(int i = 0; i < edge[cur].size(); i++){
if(ds[edge[cur][i].fi] > cst + edge[cur][i].se){
ds[edge[cur][i].fi] = cst + edge[cur][i].se;
parTem[edge[cur][i].fi].clear();
parTem[edge[cur][i].fi].push_back(cur);
pq.push({cst + edge[cur][i].se, edge[cur][i].fi});
}else if(ds[edge[cur][i].fi] == cst + edge[cur][i].se){
parTem[edge[cur][i].fi].push_back(cur);
}
}
}
}
memset(visited, 0, sizeof(visited));
queue<long long int> qi;
qi.push(t);
while(!qi.empty()){
long long int k = qi.front();
qi.pop();
if(!visited[k]){
visited[k] = true;
par[k] = parTem[k];
for(int i = 0; i < par[k].size(); i++){
qi.push(par[k][i]);
}
}
}
for(int i = 0; i <= n; i++){
dus[i] = du[i];
dvs[i] = dv[i];
}
memset(visited, 0, sizeof(visited));
pathU(t);
memset(visited, 0, sizeof(visited));
pathV(t);
long long int res = 1e16;
for(int i = 1; i <= n; i++){
res = min(res, dus[i] + dv[i]);
res = min(res, du[i] + dvs[i]);
}
cout << res << endl;
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(NULL);
int t = 1;
while(t--){
solve();
}
return 0;
}
