#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#define D(x...) printf(x)
#else
#define D(x...)
#endif
typedef long long ll;
int n;
vector<pair<int, int> > adj[500010];
int iscentroid[500010];
int seen[500010], upto;
int sz[500010];
ll closest[500010];
pair<int, ll> mycentroids[500010][20];
int findsz(int a, int p = -1)
{
seen[a] = upto;
sz[a] = 1;
for (auto b : adj[a])
{
if (b.first != p && !iscentroid[b.first]) sz[a] += findsz(b.first, a);
}
return sz[a];
}
ll len = 0;
void dfslen(int a, int c, int p = -1, ll len = 0)
{
mycentroids[a][iscentroid[c]] = { c, len };
D("%d belongs to %d, dis %lld\n", a, c, len);
for (auto b : adj[a])
{
if (!iscentroid[b.first] && b.first != p)
{
dfslen(b.first, c, a, len+b.second);
}
}
}
int findcentroid(int a, int above = 0, int p = -1)
{
if (!above) findsz(a);
int sumchildren = above+1, mxchild = above;
for (auto b : adj[a])
{
if (b.first != p && !iscentroid[b.first])
{
mxchild = max(mxchild, sz[b.first]);
sumchildren += sz[b.first];
}
}
if (mxchild <= (sumchildren)/2)
{
// is a centroid
iscentroid[a] = upto;
dfslen(a, a);
return a;
}
for (auto b : adj[a])
{
if (b.first != p && !iscentroid[b.first] && sz[b.first] == mxchild)
{
return findcentroid(b.first, sumchildren-sz[b.first], a);
}
}
assert(0); // what a shame
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
for (int i = 0; i < n-1; i++)
{
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
for (int i = 0; i < n; i++) fill_n(mycentroids[i], 20, make_pair(0, 1e15));
for (int f = 0; f < 20; f++)
{
upto++;
for (int i = 0; i < n; i++)
{
if (seen[i] != upto && !iscentroid[i])
{
findcentroid(i);
}
}
}
fill_n(closest, n, 1e15);
}
ll Query(int s, int x[], int t, int y[])
{
ll ans = 1e15;
for (int i = 0; i < s; i++) for (int j = 0; j < 20; j++)
{
auto c = mycentroids[x[i]][j];
closest[c.first] = min(closest[c.first], c.second);
}
for (int i = 0; i < t; i++) for (int j = 0; j < 20; j++)
{
auto c = mycentroids[y[i]][j];
ans = min(ans, closest[c.first]+c.second);
}
for (int i = 0; i < s; i++) for (int j = 0; j < 20; j++)
{
auto c = mycentroids[x[i]][j];
closest[c.first] = 1e15;
}
return ans;
}
