#include<bits/stdc++.h>
using namespace std;
#define ll long long
const ll MAXN = 100000;
const ll INF = 1e9*MAXN+7;
vector<pair<ll,ll>> adj[MAXN+7];
vector<ll> trace[MAXN+7];
vector<ll> zero(MAXN+7);
map<pair<ll,ll>,ll> zero_edge;
ll uuu,vvv,nnn;
ll ans=INF;
void dijkstra2(){
ll n=nnn;
ll s=uuu;
ll t=vvv;
vector<ll> d(n+7, INF);
vector<ll> p(n+7, -1);
d[s] = 0;
using pii = pair<ll, ll>;
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, s});
while (!q.empty()) {
ll v = q.top().second;
ll d_v = q.top().first;
q.pop();
if (d_v != d[v])
continue;
for (auto edge : adj[v]) {
ll to = edge.first;
ll len = edge.second;
if(zero_edge[{v,to}]==1){
len=0;
}
if (d[v] + len < d[to]) {
d[to] = d[v] + len;
p[to] = v;
q.push({d[to], to});
}
}
}
ans=min(ans,d[t]);
return;
}
vector<ll> path;
void dfs(ll s,ll v){
if(v==s){
// for(auto k : path){
// cout<<k<<" ";
// }cout<<"\n";
dijkstra2();
return;
}
for(auto k : trace[v]){
if(zero[k]==1)continue;
path.push_back(v);
zero[k]=1;
zero_edge[{v,k}]=1;
zero_edge[{k,v}]=1;
dfs(s,k);
path.pop_back();
zero[k]=0;
zero_edge[{v,k}]=0;
zero_edge[{k,v}]=0;
}
return;
}
void dijkstra1(ll n, ll s, ll t){
vector<ll> d(n+7, INF);
vector<ll> p(n+7, -1);
d[s] = 0;
using pii = pair<ll, ll>;
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, s});
while (!q.empty()) {
ll v = q.top().second;
ll d_v = q.top().first;
q.pop();
if (d_v != d[v])
continue;
for (auto edge : adj[v]) {
ll to = edge.first;
ll len = edge.second;
if (d[v] + len < d[to]) {
d[to] = d[v] + len;
p[to] = v;
q.push({d[to], to});
trace[to].clear();
trace[to].push_back(v);
}else if(d[v]+len == d[to]){
trace[to].push_back(v);
}
}
}
return;
}
int main(){
ll n,m,s,t,u,v;
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(ll i=0; i<m; i++){
ll a,b,w;
cin>>a>>b>>w;
adj[b].push_back({a,w});
adj[a].push_back({b,w});
}
uuu=u;
vvv=v;
nnn=n;
dijkstra1(n, s, t);
dfs(s, t);
cout<<ans<<"\n";
return 0;
}
