#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2,fma")
#define ll long long
#define pb push_back
#define eb emplace_back
#define pu push
#define ins insert
#define fi first
#define se second
#define all(a) a.begin(),a.end()
#define bruh ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fu(x,a,b) for (auto x=a;x<=b;x++)
#define fd(x,a,b) for (auto x=a;x>=b;x--)
// #define int ll
using namespace std;
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
/*
Competitive Programming notes that I need to study & fix my dumbass self:
1. Coding:
- Always be sure to check the memory of arrays (maybe use vectors), for loops
- Always try to maximize the memory if possible, even if you are going for subtasks
- Do not exploit #define int long long, it will kill you
2. Stress:
- Always try generating big testcases and try if they run
3. Time management:
- Don't overcommit or undercommit, always spend a certain amount of time to think a problem, don't just look at it and say I'm fucked
- Do not spend too much time coding brute-force solutions, they should be easily-codable solutions that don't take up too much time
Time management schedule:
Offline / LAH days (4 problems - 3h):
15' thinking of solution / idea
1. no idea: skip
2. yes idea: continue thinking for <= 15'
+ implementing: <= 20'
+ brute-force: <= 5'
+ test generator: <= 5'
I hate offline because I am dumb
*/
typedef pair<int, int> ii;
const int N = 1e6+5;
const int M = 20+5;
const int MAXM = (1<<20) + 5;
const int B = 750;
const int mod = 1e9+7;
const int inf = 2e9;
using cd = complex<double>;
const long double PI = acos(-1);
int power(int a,int b) {ll x = 1;if (a >= mod) a%=mod; while (b) {if (b & 1) x = x*a % mod;a = a*a % mod;b>>=1;}return x;}
int n, m, s, t;
vector<ii> adj[N];
vector<pair<ii, int>> e;
vector<int> nodes;
int needed[2*M][2*M], dist[2*M][2*M];
int dp[M][MAXM];
int up[N][M];
int h[N], par[N], xr[N];
void dfs(int u, int p) {
par[u] = p;
up[u][0] = p;
for (int i = 1; i < M; i++) up[u][i] = up[up[u][i-1]][i-1];
for (auto i : adj[u])
{
int v = i.fi, w = i.se;
if (v == p) continue;
xr[v] = xr[u];
if (w != -1) xr[v] ^= (1<<w);
h[v] = h[u] + 1;
dfs(v, u);
}
}
int lca(int u, int v)
{
if (h[u] < h[v]) swap(u, v);
int ou = u;
int diff = h[u] - h[v];
for (int i = 0; i < M; i++) if (diff>>i & 1) u = up[u][i];
if (u == v) return u;
for (int i = M-1; i >= 0; i--) if (up[u][i] != up[v][i]) u = up[u][i], v = up[v][i];
return up[u][0];
}
bool can(int u, int id, int mask)
{
return (mask & needed[id][u]) == needed[id][u];
}
void solve()
{
cin>>n>>s>>t;
for (int i = 1; i < n; i++)
{
int u,v,w;
cin>>u>>v>>w;
if (w) e.pb({{u, v}, w}), adj[u].pb({v, e.size()-1}), adj[v].pb({u, e.size()-1});
else adj[u].pb({v, -1}), adj[v].pb({u, -1});
}
m = e.size();
dfs(s, 0);
for (int i = 0; i < m; i++)
{
int u = e[i].fi.fi, v = e[i].fi.se, w = e[i].se;
if (h[u] > h[v]) swap(e[i].fi.fi, e[i].fi.se);
}
for (int i = 0; i < 2*m+2; i++)
{
int cur = (i < m ? e[i].fi.fi : (i == m ? s : (i == m+1 ? t : e[i-(m+2)].se)));
for (int j = 0; j < 2*m+2; j++)
{
int nxt = (j < m ? e[j].fi.fi : (j == m ? s : (j == m+1 ? t : e[j-(m+2)].se)));
int x = lca(cur, nxt);
dist[i][j] = h[cur] + h[nxt] - 2 * h[x];
needed[i][j] = xr[cur] ^ xr[nxt];
}
}
for (int i = 0; i < (1<<m); i++) for (int j = 0; j < m+2; j++) dp[j][i] = inf;
dp[m][0] = 0;
for (int mask = 0; mask < (1<<m); mask++)
{
for (int i = 0; i < m+1; i++)
{
if (dp[i][mask] == inf) continue;
for (int j = 0; j < m+2; j++) {
if (j == m) continue;
if (j < m)
{
if (mask>>j & 1) continue;
// cout<<cur<<" "<<j+m+2<<" "<<w<<" "<<j<<" "<<mask<<endl;
if (can(i, j+m+2, mask) && can(j+m+2, j, mask))
{
// cout<<cur<<" "<<j+m+2<<" "<<w<<" "<<j<<" "<<mask<<endl;
// cout<<dist[j+m+2][cur]<<" "<<dist[j][w]<<endl;
dp[j][mask ^ (1<<j)] = min(dp[j][mask^(1<<j)], dp[i][mask] + dist[j+m+2][i] + dist[j][j+m+2]);
// cout<<dp[j][mask ^ (1<<j)]<<endl;
}
} else if (j == m+1)
{
if (can(i, m+1, mask))
{
// cout<<i<<" "<<cur<<" "<<mask<<" "<<dp[i][mask]<<endl;
dp[j][mask] = min(dp[j][mask], dp[i][mask] + dist[m+1][i]);
}
}
}
}
}
// for (int i = 0; i < m+2; i++)
// {
// for (int j = 0; j < (1<<m); j++)
// {
// if (dp[i][j] == inf) cout<<-1<<" ";
// else cout<<dp[i][j]<<" ";
// }
// cout<<endl;
// }
int ans = inf;
for (int i = 0; i < (1<<m); i++) ans = min(ans, dp[m+1][i]);
if (ans == inf) cout<<-1;
else cout<<ans;
}
/*
Go through the mistakes you usually make and revise your code, for god's sake...
*/
signed main()
{
bruh
//freopen(".inp","r",stdin);
//freopen(".out","w",stdout);
int t = 1;
// cin>>t;
while (t--)
{
solve();
cout<<"\n";
}
}
