#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define lll __ll128
#define sza(x) ((ll)x.size())
#define all(a) (a).begin(), (a).end()
#define pb push_back
#define pll pair<ll,ll>
#ifdef DEBUG
#include "helper.h"
#else
#define dbg(...)
#endif
#define log(a) 63-__builtin_clzll(a)
const ll INF=1e18;
const ll MOD=1e9+7;
struct Fenwick {
int n;
vector<ll> bit;
Fenwick() : n(0) {}
Fenwick(int n_) { init(n_); }
void init(int n_) { n = n_; bit.assign(n+1, 0); }
// add value v at 1-based index idx
void add1(int idx, ll v) {
for (; idx <= n; idx += idx & -idx) bit[idx] += v;
}
// sum over [1..idx] where idx is 1-based
ll sum1(int idx) const {
ll s = 0;
for (; idx > 0; idx -= idx & -idx) s += bit[idx];
return s;
}
ll sumq(int idx1,int idx2){
if(idx1==1)return sum1(idx2);
return sum1(idx2)-sum1(idx1-1);
}
};
void solve() {
int n,m,s,t,u,v;
cin>>n>>m;
cin>>s>>t>>u>>v;
s--,u--,v--,t--;
vector<vector<pair<int,ll>>> edges(n);
for(int i=0;i<m;i++){
int a,b;
ll c;
cin>>a>>b>>c;
a--,b--;
edges[a].push_back({b,c});
edges[b].push_back({a,c});
}
auto dik1=[&](int s){
vector<vector<int>> par(n);
vector<ll> dist(n,INF);
dist[s]=0;
priority_queue<pair<ll,int>> pq;
pq.push({0,s});
while(!pq.empty()){
auto [c,u]=pq.top();
pq.pop();
if(dist[u]<c)continue;
for(auto [v,w]:edges[u]){
if(dist[v]>w+dist[u]){
par[v].clear();
par[v].push_back(u);
dist[v]=w+dist[u];
pq.push({dist[v],v});
}else if(dist[v]==w+dist[u]){
par[v].push_back(u);
}
}
}
return make_pair(dist,par);
};
auto dik2=[&](int s){
vector<ll> dist(n,INF);
dist[s]=0;
priority_queue<pair<ll,int>> pq;
pq.push({0,s});
while(!pq.empty()){
auto [c,u]=pq.top();
pq.pop();
if(dist[u]<c)continue;
for(auto [v,w]:edges[u]){
if(dist[v]>w+dist[u]){
dist[v]=w+dist[u];
pq.push({dist[v],v});
}else if(dist[v]==w+dist[u]){
}
}
}
return dist;
};
auto [dists,par]=dik1(s);
auto distu=dik2(u);
auto distv=dik2(v);
dbg(distv);
vector<set<int>> new_edges(n);
auto dfs1=[&](auto && dfs1,int vertex) -> void {
for(auto nei:par[vertex]){
new_edges[nei].insert(vertex);
dfs1(dfs1,nei);
}
};
dfs1(dfs1,t);
dbg(new_edges);
vector<ll> dpv(n,INF);
vector<ll> dpu(n,INF);
vector<int> inb(n);
for(auto i:new_edges){
for(auto ii:i){
inb[ii]++;
}
}
ll ans=INF;
auto dfs=[&](auto && dfs,int vertex,ll u_dis,ll v_dis) -> void {
u_dis=min(u_dis,distu[vertex]);
v_dis=min(v_dis,distv[vertex]);
ans=min(ans,u_dis+v_dis);
for(auto nei:new_edges[vertex]){
dfs(dfs,nei,u_dis,v_dis);
}
};
dfs(dfs,s,INF,INF);
dbg(dpu,dpv);
cout<<min(ans,distv[u])<<endl;
}
int32_t main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("boards.in","r",stdin);
// freopen("boards.out","w",stdout);
// cout<<1<<endl;
// dbg(deals);
// ll t;
// cin>>t;
// while(t--)
solve();
}
