#include "factories.h"
#include <iostream>
#include <vector>
#include <algorithm>
#define llong long long
const int MAXN = 5 * 1e5 + 10;
const int MAXLOG = 20 + 1;
const llong INF = 1e9 + 10;
const llong MAXW = MAXN * INF;
int n;
std::vector<std::pair<int, int>> tree[MAXN];
llong globalAns;
namespace Centroid
{
llong sz[MAXN];
bool vis[MAXN];
llong centroidPar[MAXN][MAXLOG];
llong centroidDist[MAXN][MAXLOG];
llong best[MAXN], best2[MAXN];
void findSize(int node, int par)
{
sz[node] = 1;
for(const auto& [child, w] : tree[node])
{
if(child == par || vis[child]) continue;
findSize(child, node);
sz[node] += sz[child];
}
}
int findCentroid(int node, int par, int globalSize)
{
for(const auto& [child, w] : tree[node])
{
if(child == par || vis[child]) continue;
if(sz[child] * 2 > globalSize) return findCentroid(child, node, globalSize);
}
return node;
}
void calculateDist(int node, int par, int centroid, llong currDist, int level)
{
centroidPar[node][level] = centroid;
centroidDist[node][level] = currDist;
for(const auto& [child, w] : tree[node])
{
if(child == par || vis[child]) continue;
calculateDist(child, node, centroid, currDist + w, level);
}
}
void decompose(int node, int level)
{
findSize(node, -1);
int cntr = findCentroid(node, -1, sz[node]);
vis[cntr] = 1;
calculateDist(cntr, -1, cntr, 0, level);
for(const auto& [child, w] : tree[cntr])
{
if(vis[child]) continue;
decompose(child, level + 1);
}
}
void build()
{
std::fill(best, best + MAXN, MAXW);
decompose(1, 0);
}
void setNode(int node)
{
for(int level = 0 ; level < MAXLOG ; ++level)
{
llong cntr = centroidPar[node][level];
if(cntr == 0)
{
break;
}
best[cntr] = MAXW;
}
}
void set(int S, int X[], int T, int Y[])
{
for(int i = 0 ; i < S ; ++i)
{
setNode(X[i] + 1);
}
for(int i = 0 ; i < T ; ++i)
{
setNode(Y[i] + 1);
}
globalAns = MAXW;
}
void putColor(int node, int clr)
{
for(int level = 0 ; level < MAXLOG ; ++level)
{
llong cntr = centroidPar[node][level];
llong dist = centroidDist[node][level];
if(cntr == 0)
{
break;
}
if(clr == 1)
{
best[cntr] = std::min(best[cntr], dist);
}
else
{
globalAns = std::min(globalAns, best[cntr] + dist);
}
}
}
};
void Init(int N, int A[], int B[], int D[])
{
n = N;
for(int i = 0 ; i < n - 1 ; ++i)
{
tree[A[i] + 1].push_back({B[i] + 1, D[i]});
tree[B[i] + 1].push_back({A[i] + 1, D[i]});
}
Centroid::build();
}
long long Query(int S, int X[], int T, int Y[])
{
Centroid::set(S, X, T, Y);
for(int i = 0 ; i < S ; ++i)
{
Centroid::putColor(X[i] + 1, 1);
}
for(int i = 0 ; i < T ; ++i)
{
Centroid::putColor(Y[i] + 1, 2);
}
return globalAns;
}
