#include <bits/stdc++.h>
using namespace std;
#define all(x) x.begin() , x.end()
#define pii pair<int,int>
#define pll pair<ll,ll>
#define F first
#define S second
#define wall cerr<<"------------------------"<<endl
typedef long long ll;
const ll INF = 1e9;
const ll maxn = 2e6 + 10;
const ll mod = 1e9 + 7;
int n , m , k , ST , EN;
int h[maxn] , p[maxn] , st[maxn] , en[maxn];
int a[maxn<<1] , rmq[maxn<<1][22] , ps_rmq[maxn<<1][22] , rrmq[maxn<<1][22] , ps_rrmq[maxn<<1][22] , len[maxn<<1];
vector<int> g[maxn] , LSA;
bool mrk[maxn];
void DFS(int v)
{
mrk[v] = 1;
LSA.push_back(v);
st[v] = LSA.size()-1;
for(auto u : g[v]){
if(mrk[u]==1)continue;
p[u] = v;
h[u] = h[v]+1;
DFS(u);
LSA.push_back(v);
}
en[v] = LSA.size()-1;
}
inline void pre_LCA()
{
LSA.push_back(0);
p[ST] = -1;
h[ST] = 1;
DFS(ST);
m = LSA.size()-1;
//wall;
for(int i=1; i<=m; i++){
a[i] = h[LSA[i]];
}
for(int j=0; j<=21; j++){
for(int i=1; i<=m; i++){
if(j==0){
rmq[i][j] = a[i];
rrmq[i][j] = a[i];
ps_rmq[i][j] = i;
ps_rrmq[i][j] = i;
continue;
}
if((i+(1<<j)-1)<=m){
rmq[i][j] = rmq[i][j-1];
ps_rmq[i][j] = ps_rmq[i][j-1];
if(rmq[i][j-1] > rmq[i+(1<<(j-1))][j-1]){
rmq[i][j] = rmq[i+(1<<(j-1))][j-1];
ps_rmq[i][j] = ps_rmq[i+(1<<(j-1))][j-1];
}
}
if((i-(1<<j)+1)>0){
rrmq[i][j] = rrmq[i][j-1];
ps_rrmq[i][j] = ps_rrmq[i][j-1];
if(rrmq[i][j-1] > rrmq[i-(1<<(j-1))][j-1]){
rrmq[i][j] = rrmq[i-(1<<(j-1))][j-1];
ps_rrmq[i][j] = ps_rrmq[i-(1<<(j-1))][j-1];
}
}
}
}
int PS = 0;
for(int i=1; i<=m; i++){
if(((1<<PS)<<1)<=i){
PS++;
}
len[i] = PS;
}
}//OK
inline int LCA(int v , int u)
{
int l = min(st[v],st[u]) , r=max(st[v],st[u]);
int ln = len[r-l+1];
int x = rmq[l][ln] , y = rrmq[r][ln];
if(x < y){
int pos = ps_rmq[l][ln];
return LSA[pos];
}else{
int pos = ps_rrmq[r][ln];
return LSA[pos];
}
}
inline int DIS(int v , int u)
{
if(v<1 || n<v || v<u || n<u)return INF;
return (h[v]+h[u]-h[LCA(v,u)]-h[LCA(v,u)]);
}
vector<pii> eg[maxn];
bool mark[maxn];
int req[maxn];
map<int,int> MP[maxn];
void dfs(int v)
{
mark[v] = 1;
for(auto e : eg[v]){
int u=e.F , w=e.S;
if(mark[u]==1)continue;
p[u] = v;
req[u] = req[v];
if(w!=0){
int x = MP[v][u];
req[u] |= (1<<x);
}
dfs(u);
}
}
vector<pair<int,pii>> EG;
int dp[1<<22][30];
int main()
{
ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL);
cin>>n>>ST>>EN;
int ps = 0;
for(int i=1; i<n; i++){
int v,u,w; cin>>v>>u>>w;
if(w!=0){
MP[v][u] = ps;
MP[u][v] = ps;
ps++;
EG.push_back({w,{v,u}});
}
eg[v].push_back({u,w});
eg[u].push_back({v,w});
g[v].push_back(u);
g[u].push_back(v);
}
/**/
pre_LCA();
for(int i=1; i<=n; i++){
p[i] = -1;
}
dfs(ST);
for(int i=1; i<(1<<((int)EG.size()))+(1<<((int)EG.size())); i++){
for(int j=0; j<((int)EG.size())+1; j++){
dp[i][j] = INF;
}
}
for(int i=1; i<(1<<((int)EG.size())); i++){
int pos = i;
while(pos>0){
int j = __builtin_ctz(pos);
pos -= (1<<j);
int x = i^(1<<j);
int V=EG[j].S.F , U=EG[j].S.S , W=EG[j].F;
if(req[W]!=(req[W]&x))continue;
if(req[V]!=(req[V]&x) && req[U]!=(req[U]&x))continue;
if(x==0){
dp[i][j] = DIS(ST,W) + min(DIS(W,V),DIS(W,U));
continue;
}
int POS=i;
while(POS>0){
int f = __builtin_ctz(POS);
POS -= 1<<f;
int v=EG[f].S.F , u=EG[f].S.S;
int D1=DIS(ST,v) , D2=DIS(ST,u);
if(D1>D2){
swap(v,u);
}
dp[i][j] = min(dp[i][j] , dp[x][f]+DIS(v,W)+min(DIS(W,V),DIS(W,U)) );
}
}
}
/***********************************/
ps = ((int)EG.size());
eg[EN].push_back({n+1,EN});
eg[n+1].push_back({EN,EN});
MP[EN][n+1] = ps;
MP[EN][n+1] = ps;
EG.push_back({EN,{EN,n+1}});
for(int i=(1<<ps); i<(1<<(ps+1)); i++){
int j = ps;
int x = i^(1<<j);
int V=EG[j].S.F , U=EG[j].S.S , W=EG[j].F;
if(req[W]!=(req[W]&x))continue;
if(req[V]!=(req[V]&x) && req[U]!=(req[U]&x))continue;
if(x==0){
dp[i][j] = DIS(ST,W) + min(DIS(W,V),DIS(W,U));
continue;
}
int POS=i;
while(POS>0){
int f = __builtin_ctz(POS);
POS -= 1<<f;
int v=EG[f].S.F , u=EG[f].S.S;
int D1=DIS(ST,v) , D2=DIS(ST,u);
if(D1>D2){
swap(v,u);
}
dp[i][j] = min(dp[i][j] , dp[x][f]+DIS(v,W)+min(DIS(W,V),DIS(W,U)) );
}
}
int ans = INF;
for(int i=(1<<ps); i<(1<<(ps+1)); i++){
ans = min(ans , dp[i][ps]);
}
if(ans==INF){
cout<<-1;
return 0;
}
cout<<ans;
return 0;
}
/*
3
1 3
1 2 3
1 3 2
*/
/*
10
1 10
1 2 0
2 3 0
3 4 0
4 5 2
2 6 4
2 7 0
7 8 5
8 9 6
9 10 0
ans = 15
*/
/**
4
1 4
1 2 0
1 3 2
3 4 1
ans = 4;
*/
/*
5
3 1
1 2 5
2 3 4
3 4 0
4 5 2
ans = 10;
*/
Compilation message
/usr/bin/ld: failed to convert GOTPCREL relocation; relink with --no-relax
collect2: error: ld returned 1 exit status
