/*
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░ ░░░░░░░░ ░░░░░ ░ ░ ░░░░ ░░░░░ ░░░░░░ ░░░░
▒▒▒▒▒▒ ▒ ▒▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒ ▒▒▒ ▒▒▒▒ ▒▒▒ ▒▒▒▒ ▒▒
▒▒▒▒▒ ▒▒ ▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒▒ ▒▒▒▒ ▒ ▒▒▒▒▒▒▒▒ ▒ ▒▒▒▒ ▒▒
▓▓▓▓ ▓▓▓ ▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓ ▓▓▓▓▓▓▓▓ ▓ ▓ ▓▓▓▓▓▓
▓▓▓ ▓ ▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓ ▓ ▓▓▓▓▓▓▓▓ ▓ ▓▓ ▓▓▓▓
▓▓ ▓▓▓▓▓▓▓ ▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓▓ ▓▓▓▓ ▓▓▓ ▓▓▓▓▓ ▓▓ ▓▓▓▓ ▓▓
█ █████████ ███ ████████ █████ ████ █████ ██████ ██████
███████████████████████████████████████████████████████████████████████████████
▄▄▄ ███▄ █ ███▄ █ ██░ ██ ▄▄▄ ▄▄▄ ▄▄▄█████▓
▒████▄ ██ ▀█ █ ██ ▀█ █ ▒▓██░ ██ ▒████▄ ▒████▄ ▓ ██▒ ▓▒
▒██ ▀█▄ ▓██ ▀█ ██▒▓██ ▀█ ██▒░▒██▀▀██ ▒██ ▀█▄ ▒██ ▀█▄ ▒ ▓██░ ▒░
░██▄▄▄▄██▓██▒ ▐▌██▒▓██▒ ▐▌██▒ ░▓█ ░██ ░██▄▄▄▄██░██▄▄▄▄██░ ▓██▓ ░
▓█ ▓██▒██░ ▓██░▒██░ ▓██░ ░▓█▒░██▓ ▓█ ▓██ ▓█ ▓██ ▒██▒ ░
▒▒ ▓▒█░ ▒░ ▒ ▒ ░ ▒░ ▒ ▒ ▒ ░░▒░▒ ▒▒ ▓▒█ ▒▒ ▓▒█ ▒ ░░
░ ▒▒ ░ ░░ ░ ▒░░ ░░ ░ ▒░ ▒ ░▒░ ░ ░ ▒▒ ░ ▒▒ ░
░ ▒ ░ ░ ░ ░ ░ ░ ░ ░░ ░ ░ ▒ ░ ▒ ░ ░
░ ░ ░ ░ ░ ░ ░ ░
*/
//#include <bits/BaoMinhTranc++.h>
#include <bits/stdc++.h>
#define int int64_t
//#define ll int64_t
#define ld long double
#define ii pair<int,int>
#define iii pair<int,ii>
#define fi first
#define se second
#define ALL(x) x.begin(),x.end()
#define ALLr(x) x.rbegin(),x.rend()
#define upgrade ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define name "youreagoodmanarthur"
using namespace std;
const int Max=1<<20;
const int N=1e5+3;
const int INF=1e18;
const int MOD=998244353;
const int MOD2=1e9+8;
const int base=26;
const int LOG=32;
template<class X,class Y>
bool minimize(X& x,const Y& y)
{
if(x>y){
x=y;
return 1;
}return 0;
}
template<class X,class Y>
bool maximize(X& x,const Y& y)
{
if(x<y){
x=y;
return 1;
}return 0;
}
int n,m,s,t,u,v;
vector<ii> g[N];
priority_queue<ii,vector<ii>,greater<ii>> q;
int dist[3][N];
vector<int> tail[3][N];
vector<int> dag;
vector<int> g_dag[N];
bool visited[N];
ii dp[N];
bool cmp(int x,int y){return dist[0][x]>dist[0][y];}
void dijk(int st,int slot)
{
for(int i=1;i<=n;i++)dist[slot][i]=INF;
dist[slot][st]=0;
q.push({0,st});
while(!q.empty()){
int u=q.top().se,cost=q.top().fi;
q.pop();
if(dist[slot][u]<cost)continue;
for(ii x:g[u]){
int v=x.fi,w=x.se;
if(minimize(dist[slot][v],cost+w)){
tail[slot][v].clear();
q.push({cost+w,v});
}
if(cost+w == dist[slot][v])tail[slot][v].push_back(u);
}
}
}
void build()
{
dag.push_back(t);
queue<int> sontung;
sontung.push(t);
visited[t]=1;
while(!sontung.empty()){
int x=sontung.front();
sontung.pop();
for(int y:tail[0][x]){
g_dag[y].push_back(x);
if(!visited[y]){
dag.push_back(y);
visited[y]=1;
sontung.push(y);
}
}
}
sort(ALL(dag),cmp);
}
void solve()
{
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(int _=1;_<=m;_++){
int x,y,w;cin>>x>>y>>w;
g[x].push_back({y,w});
g[y].push_back({x,w});
}
dijk(s,0);dijk(u,1);dijk(v,2);
build();
int ans=dist[1][v];
for(int x:dag){
dp[x]={dist[1][x],dist[2][x]};
for(int y:g_dag[x]){
minimize(ans,dist[1][x]+dp[y].se);
minimize(ans,dist[2][x]+dp[y].fi);
minimize(dp[x].fi,dp[y].fi);
minimize(dp[x].se,dp[y].se);
}
}
cout<<ans;
}
void prepare()
{
}
signed main()
{
upgrade
if(fopen(name".INP","r")){
freopen(name".INP","r",stdin);
freopen(name".OUT","w",stdout);
}
prepare();
int test=1;
// cin>>test;
while(test--)solve();
return 0;
}
/*
░▓▓
░▒▒▒ ░▒▒▒▒▒▒░░░ ░▓▓
▓▒ ▒▓▓▓▓▓▓▓▓▓▓▓▓▒ ░▓▓▓▓▓▓▓▓▓▓▓▒░ ▒▓▓▒ ▒▒▒▒░ ░░░░▒░▒▒▒▒▒▒ ░▓▓ ░░▒▒▒▒▒░░
▒▓▓▒ ▒▓▓░ ░▓▓▒ ░▓▓▓▒ ░▒▓▓░░▓▓▒ ▒▒▒ ▒▒▒▒▒▒░░░▒▒▒▒▒▒▒▒▒▒▒░ ░▓▓▓▒▒▒▒▒▒▒▒▒▒▓▒▒░
▓▓▓▓▒ ░▓▓▒ ▒▓▓▒ ░▓▓▓░ ░▒░ ░▒▒▒▒▒▒▒▒ ▒▒▒░ ▒▒▒ ░▓▓
░▓▓░ ▓▓▓ ░▒▒▒ ▒▒▒ ░▒▒ ▒▓▒
▒▓▒ ▓▓▓ ░░ ▒▒░ ▒▒▒ ▒▒░ ▓▓▓
░▓▒ ░▓▓▓ ░▒ ▒▒░ ▒▒░ ▒▒░ ▒▒▒ ▓▓▓░
░▓▒ ░▓▓▓▒ ▒▒▒ ░▒▒▒░ ░▒▒░ ░▒▒ ▒▒▒ ▓▓▓▒
▒▓▒ ▓▓▓░ ░ ▒▒░ ▒▒▒ ▒▒▒▒▒▒▒▒░ ▒▒▒▒▒▒▒▒ ░▓▓▓
░▓▓▒ ▒▓▓▓▒ ░▓▓▓▓▒ ░▒▒ ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒░ ▒▒▒░ ░▓▓▓
░▒ ░▓▓▓▓▓▓▒░ ▒▓▓▓▓▓▒▓▓▒ ▒▒▒▒▒▒▒░ ░▒▒▒▒▒▒▒░ ▓▓▓▓▒▒ ▒▓▓▓▓
░░▓▓▓▓▓▓▓▓▒░░ ▒▓▒ ░▒▒▒▒░ ░▒▓▓▓▓▓▓▓▓▒░
▒▓▓░ ▒▒░
▓▒ ▒▓▓░ ▒▒▒░
▓▓▒ ░▓▓▒ ░▒▒▒▒
▓▓▓░ ▒▓▓▓ ░▒▒▒
░▓▓▓▓░ ░▓▓▓▒
░▓▓▓▓▓▒▒░░░ ░░░▒▒▓▓▓▓░
░▒▒▒▒▒▒▒▒░
*/
