#include <bits/stdc++.h>
#define ld long double
#define endl "\n"
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define pb(x) push_back(x)
#define mp(a,b) make_pair(a,b)
#define ms(v,x) memset(v,x,sizeof(v))
#define all(v) v.begin(),v.end()
#define ff first
#define ss second
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define per(i, a, b) for(int i = b-1; i>=a ; i--)
#define trav(a, x) for(auto& a : x)
#define allin(a , x) for(auto a : x)
#define td(v) v.begin(),v.end()
#define sz(v) (int)v.size()
//#define int long long
using namespace std;
typedef vector<int> vi;
#define y1 abacaba
#define left sefude
#define db(x) cerr << #x <<" == "<<x << endl;
#define db2(x,y) cerr<<#x <<" == "<<x<<", "<<#y<<" == "<<y<<endl;
#define db3(x,y,z) cerr << #x<<" == "<<x<<", "<<#y<<" == "<<y<<", "<<#z<<" == "<<z<<endl;
typedef long long ll;
typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
inline ll mod(ll n, ll m ){ ll ret = n%m; if(ret < 0) ret += m; return ret; }
ll gcd(ll a, ll b){return (b == 0LL ? a : gcd(b, a%b));}
ll exp(ll a,ll b,ll m){
if(b==0LL) return 1LL;
if(b==1LL) return mod(a,m);
ll k = mod(exp(a,b/2,m),m);
if(b&1LL){
return mod(a*mod(k*k,m),m);
}
else return mod(k*k,m);
}
const int N = 1e5 + 100;
ll d[N];
typedef pair<ll,ll> pll;
vector<pll> g[N];
int vis[N];
int SLA=0;
map<pii,int> mp;
int n;
ll dist[N][4];
struct coisa{
int v,j;
ll d;
coisa(){}
coisa(ll d,int v,int j):d(d),v(v),j(j){}
bool operator<(const coisa& o )const{
return d > o.d;
}
};
bool mark[N][4];
struct edge{
int v,w,j;
edge(){}
edge(int v,int w,int j):v(v),w(w),j(j){}
};
vector<edge> adj[N];
void DJ2(int U,int V){
rep(i,0,N)rep(j,0,4){
dist[i][j] = 1e18;
mark[i][j] = 0;
}
dist[U][0] = 0;
priority_queue<coisa> pq;
pq.push(coisa(0,U,0));
while(!pq.empty()){
int cur = pq.top().v,j = pq.top().j;
pq.pop();
if(mark[cur][j])continue;
mark[cur][j]=1;
for(auto e : adj[cur]){
int to = e.v;
ll w = e.w;
int t = e.j;
if(t == 3){
// ababa
if(j==0 and dist[to][0] > dist[cur][j] + w){
pq.push(coisa(dist[to][0] = dist[cur][j] + w,to,0));
}
if(dist[to][3] > dist[cur][j] + w){
pq.push(coisa(dist[to][3] = dist[cur][j] + w,to,3));
}
}else if(t==1){
// only j == 0 or j == 1 can pick
if(j ==0 || j == 1){
if(dist[to][1] > dist[cur][j] + w){
pq.push(coisa(dist[to][1] = dist[cur][j] + w,to,1));
}
}
}else if(t==2){
// only j == 0 or j == 2 can pick
if(j == 0 || j == 2){
if(dist[to][2] > dist[cur][j] + w){
pq.push(coisa(dist[to][2] = dist[cur][j] + w,to,2));
}
}
}
}
}
cout << min({dist[V][0],dist[V][1],
dist[V][2],dist[V][3]}) << endl;
}
void DJ(int S,int T){
for(int i=0;i<N;i++)d[i] = 1e18,vis[i]=0;
d[S] = 0;
mp.clear();
priority_queue<pll,vector<pll>,greater<pll> > pq;
pq.push(pll(d[S],S));
while(!pq.empty()){
int cur = pq.top().ss;
if(d[cur]!=pq.top().ff){
pq.pop();continue;
}
pq.pop();
for(auto to : g[cur]){
if(d[to.ff] > d[cur] + to.ss){
d[to.ff] = d[cur] + to.ss;
pq.push(pll(d[to.ff],to.ff));
}
}
}
queue<int> q;
q.push(T);
while(!q.empty()){
int cur = q.front();q.pop();
vis[cur] = 1;
for(auto to : g[cur]){
if(d[to.ff] + to.ss == d[cur]){
mp[pii(to.ff,cur)] = 1;
if(!vis[to.ff]){
vis[to.ff] = 1;
q.push(to.ff);
}
}
}
}
rep(i,0,N){
int cur = i;
for(auto to : g[i]){
if(mp[pii(to.ff,cur)]){
adj[i].pb(edge(to.ff,0,1));
}else if(mp[pii(cur,to.ff)]){
adj[i].pb(edge(to.ff,0,2));
}
adj[i].pb(edge(to.ff,to.ss,3));
}
}
}
int32_t main(){
fastio;
int m;
cin >> n >> m;
int S,T;
cin >> S >> T;
int U,V;
cin >> U >> V;
for(int i=0;i<m;i++){
int a,b,c;
cin >> a >> b >> c;
g[a].pb(pii(b,c));
g[b].pb(pii(a,c));
}
DJ(S,T);
DJ2(U,V);
// math -> gcd it all
// Did u check N=1? Did you switch N,M?
}
