#include <bits/stdc++.h>
using namespace std;
vector<pair<int,int>> adjlst[100100];
vector<pair<int,int>> fadj[100100];
vector<pair<int,int>> badj[100100];
int N,M;
int s,t;
int u,v;
int a,b,h;
long long int du[100100],dv[100100],ds[100100],dt[100100];
bool visited[100100];
priority_queue<pair<long long int, int>, vector<pair<long long int, int>>,greater<pair<long long int, int>>> pq;
int main(){
scanf(" %d",&N);
scanf(" %d",&M);
scanf(" %d",&s);
scanf(" %d",&t);
scanf(" %d",&u);
scanf(" %d",&v);
s--;
t--;
u--;
v--;
for(int i = 0; i < N; i++){
du[i] = 1100100100100100100;
dv[i] = 1100100100100100100;
ds[i] = 1100100100100100100;
dt[i] = 1100100100100100100;
visited[i] = false;
}
for(int i = 0; i < M; i++){
scanf(" %d",&a);
scanf(" %d",&b);
scanf(" %d",&h);
a--;
b--;
adjlst[a].push_back(make_pair(b,h));
adjlst[b].push_back(make_pair(a,h));
}
pq.push(make_pair(0,u));
du[u] = 0;
while(!pq.empty()){
int i = pq.top().second;
long long int d = pq.top().first;
pq.pop();
if(!visited[i]){
visited[i] = true;
for(pair<int, int> j : adjlst[i]){
if(d + j.second < du[j.first]){
du[j.first] = d + j.second;
pq.push(make_pair(d + j.second, j.first));
}
}
}
}
for(int i = 0; i < N; i++) visited[i] = false;
pq.push(make_pair(0,v));
dv[v] = 0;
while(!pq.empty()){
int i = pq.top().second;
long long int d = pq.top().first;
pq.pop();
if(!visited[i]){
visited[i] = true;
for(pair<int, int> j : adjlst[i]){
if(d + j.second < dv[j.first]){
dv[j.first] = d + j.second;
pq.push(make_pair(d + j.second, j.first));
}
}
}
}
for(int i = 0; i < N; i++) visited[i] = false;
pq.push(make_pair(0,s));
ds[s] = 0;
while(!pq.empty()){
int i = pq.top().second;
long long int d = pq.top().first;
pq.pop();
if(!visited[i]){
visited[i] = true;
for(pair<int, int> j : adjlst[i]){
if(d + j.second < ds[j.first]){
ds[j.first] = d + j.second;
pq.push(make_pair(d + j.second, j.first));
}
}
}
}
for(int i = 0; i < N; i++) visited[i] = false;
pq.push(make_pair(0,t));
dt[t] = 0;
while(!pq.empty()){
int i = pq.top().second;
long long int d = pq.top().first;
pq.pop();
if(!visited[i]){
visited[i] = true;
for(pair<int, int> j : adjlst[i]){
if(d + j.second < dt[j.first]){
dt[j.first] = d + j.second;
pq.push(make_pair(d + j.second, j.first));
}
}
}
}
long long int STD = dt[s];
long long int meen[N];
vector<pair<long long int, int>> topo;
for(int i = 0; i < N; i++) topo.emplace_back(ds[i],i);
for(int i = 0; i < N; i++) meen[i] = 1100100100100100100;
long long int big = du[v];
//printf("%lld ",STD);
sort(topo.begin(),topo.end());
for(int i = 0; i < topo.size(); i++){
int j = topo[i].second;
if(ds[j] + dt[j] > STD) continue;
meen[j] = min(meen[j],du[j]);
big = min(big,meen[j] + dv[j]);
for(pair<int,int> ii : adjlst[j]){
int k = ii.first;
if(ii.second + ds[j] + dt[k] == STD) meen[k] = min(meen[k],meen[j]);
}
}
for(int i = 0; i < N; i++) meen[i] = 1100100100100100100;
reverse(topo.begin(),topo.end());
for(int i = 0; i < topo.size(); i++){
int j = topo[i].second;
if(ds[j] + dt[j] > STD) continue;
meen[j] = min(meen[j],du[j]);
big = min(big,meen[j] + dv[j]);
for(pair<int,int> ii : adjlst[j]){
int k = ii.first;
if(ii.second + dt[j] + ds[k] == STD) meen[k] = min(meen[k],meen[j]);
}
}
printf("%lld",big);
}
