/*
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
*/
#include<bits/stdc++.h>
#define int long long
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define eb emplace_back
#define PI 3.14159265359
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define BIT(x,i) (1&((x)>>(i)))
#define MASK(x) (1LL<<(x))
#define task "tnc"
using namespace std;
typedef long long ll;
const ll INF=1e18;
const int maxn=1e5+5;
const int mod=1e9+7;
const int mo=998244353;
using pi=pair<ll,ll>;
using vi=vector<ll>;
using pii=pair<pair<ll,ll>,ll>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int n,m;
struct Edge{
int u,v,w,id;
Edge(){}
Edge(int _u,int _v,int _w,int _id){
u=_u;
v=_v;
w=_w;
id=_id;
}
}ed[maxn];
vector<Edge>G[maxn];
vector<pair<int,int>>trace[maxn];
vector<int>G2[maxn];
int d[maxn];
int deg[maxn];
int du[maxn];
int dv[maxn];
int dp[maxn];
int dp1[maxn];
int ok[maxn];
int s,t;
int u,v;
void DIJ(){
for(int i=1;i<=n;i++)d[i]=INF;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,s});
d[s]=0;
while(pq.size()){
pair<int,int>cha=pq.top();
pq.pop();
if(d[cha.se]!=cha.fi)continue;
for(Edge canh:G[cha.se]){
if(d[cha.second]+canh.w<d[canh.v]){
d[canh.v]=d[cha.second]+canh.w;
trace[canh.v].clear();
trace[canh.v].pb({cha.se,canh.id});
pq.push({d[canh.v],canh.v});
}
else if(d[cha.se]+canh.w==d[canh.v]){
trace[canh.v].pb({cha.se,canh.id});
}
}
}
}
void DIJ1(){
for(int i=1;i<=n;i++)du[i]=INF;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,u});
du[u]=0;
while(pq.size()){
pair<int,int>cha=pq.top();
pq.pop();
if(du[cha.se]!=cha.fi)continue;
for(Edge canh:G[cha.se]){
if(du[cha.second]+canh.w<du[canh.v]){
du[canh.v]=du[cha.second]+canh.w;
pq.push({du[canh.v],canh.v});
}
}
}
}
void DIJ2(){
for(int i=1;i<=n;i++)dv[i]=INF;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,v});
dv[v]=0;
while(pq.size()){
pair<int,int>cha=pq.top();
pq.pop();
if(dv[cha.se]!=cha.fi)continue;
for(Edge canh:G[cha.se]){
if(dv[cha.second]+canh.w<dv[canh.v]){
dv[canh.v]=dv[cha.second]+canh.w;
pq.push({dv[canh.v],canh.v});
}
}
}
}
void get(int dinh){
deg[dinh]=trace[dinh].size();
ok[dinh]=1;
for(auto v1:trace[dinh]){
G2[v1.first].pb(dinh);
if(ok[v1.first]==0){
get(v1.first);
}
}
}
signed main()
{
cin.tie(0),cout.tie(0)->sync_with_stdio(0);
//freopen(task".inp" , "r" , stdin);
//freopen(task".out" , "w" , stdout);
cin>>n>>m>>s>>t>>u>>v;
for(int i=1;i<=m;i++){
int x,y,w;
cin>>x>>y>>w;
G[x].pb(Edge(x,y,w,i));
G[y].pb(Edge(y,x,w,i));
ed[i]=Edge(x,y,w,i);
}
DIJ();
DIJ1();
DIJ2();
int ans=du[v];
get(t);
dp[s]=du[s];
queue<int>qu;
qu.push(s);
vector<int>topo;
while(qu.size()){
int dinh=qu.front();
qu.pop();
topo.pb(dinh);
for(auto canh:G2[dinh]){
deg[canh]--;
if(deg[canh]==0){
qu.push(canh);
}
}
}
for(auto dinh:topo){
dp[dinh]=du[dinh];
}
for(auto dinh:topo){
for(auto den:trace[dinh]){
dp[dinh]=min(dp[den.fi],dp[dinh]);
}
ans=min(ans,dp[dinh]+dv[dinh]);
}
reverse(topo.begin(),topo.end());
for(auto dinh:topo){
dp1[dinh]=dv[dinh];
}
for(auto dinh:topo){
for(auto den:G2[dinh]){
dp1[dinh]=min(dp1[den],dp1[dinh]);
}
ans=min(ans,dp1[dinh]+dp[dinh]);
}
cout<<ans;
return 0;
}
