#include <bits/stdc++.h>
using namespace std;
const int N = 200*1000+7;
const long long INF = 100000000000000005;
vector<pair<int,long long> > g[N];
long long dist[N];
long long ans = INF;
int n,m;
int s,t;
int U,V;
long long distu[N],distv[N];
long long dp1[N],dp2[N];
long long distt[N];
bool c[N];
int main(){
scanf("%d%d",&n,&m);
scanf("%d%d",&s,&t);
scanf("%d%d",&U,&V);
for(int i = 0;i<m;i++){
int x,y;
long long z;
scanf("%d%d%lld",&x,&y,&z);
g[x].push_back({y,z});
g[y].push_back({x,z});
}
priority_queue<pair<long long,int> > pq;
pq.push({0,s});
for(int i = 0;i<=n;i++) dist[i] = INF;
dist[s] = 0;
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(dist[to]>(-gag.first)+g[gag.second][i].second){
dist[to] = (-gag.first)+g[gag.second][i].second;
pq.push({-dist[to],to});
}
}
}
pq.push({0,t});
for(int i = 0;i<=n;i++) distt[i] = INF;
distt[t] = 0;
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(distt[to]>(-gag.first)+g[gag.second][i].second){
distt[to] = (-gag.first)+g[gag.second][i].second;
pq.push({-distt[to],to});
}
}
}
// dfs(s);
// if(all.size() == 0) assert(0);
pq.push({0,U});
for(int i = 0;i<=n;i++) distu[i] = INF;
distu[U] = 0;
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(distu[to]>(-gag.first)+g[gag.second][i].second){
distu[to] = (-gag.first)+g[gag.second][i].second;
pq.push({-distu[to],to});
}
}
}
pq.push({0,V});
for(int i = 0;i<=n;i++) distv[i] = INF;
distv[V] = 0;
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(distv[to]>(-gag.first)+g[gag.second][i].second){
distv[to] = (-gag.first)+g[gag.second][i].second;
pq.push({-distv[to],to});
}
}
}
for(int i = 0;i<=n;i++) dp1[i] = INF;
dp1[s] = distv[s];
c[s] = 1;
// cout<<dp1[s]<<endl;
pq.push({-dp1[s],s});
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(!c[to] && dp1[to]>min(-gag.first,distv[to]) && dist[t] == dist[to]+distt[to]){
dp1[to] = min(-gag.first,distv[to]);
pq.push({-dp1[to],to});
}
}
}
for(int i = 0;i<=n;i++) dp2[i] = INF;
memset(c,0,sizeof(c));
dp2[t] = distv[t];
c[t] = 1;
pq.push({-dp2[t],t});
while(!pq.empty()){
pair<long long,int> gag = pq.top();
pq.pop();
for(int i = 0;i<g[gag.second].size();i++){
int to = g[gag.second][i].first;
if(!c[to] && dp2[to]>min(-gag.first,distv[to]) && dist[t] == dist[to]+distt[to]){
dp2[to] = min(-gag.first,distv[to]);
pq.push({-dp2[to],to});
}
}
}
ans = min(distu[V],distv[U]);
for(int i = 1;i<=n;i++){
if(dist[t] == dist[i]+distt[i]){
// cout<<i<<" "<<distu[i]<<" "<<dp1[i]<<" "<<dp2[i]<<endl;
ans = min(ans,distu[i]+min(dp1[i],dp2[i]));
}
}
/*for(int i = 0;i<all.size();i++){
long long mn = INF;
long long mnn = INF;
for(int j = 0;j<all[i].size();j++){
mn = min(mn,distu[all[i][j]]);
mnn = min(mnn,distv[all[i][j]]);
}
if(mn<INF && mnn<INF)
ans = min(ans,mn+mnn);
}*/
cout<<ans<<endl;
/*for(int i = 1;i<=n;i++){
cout<<i<<" "<<dist[i]<<endl;
}*/
return 0;
}
