#include "catdog.h"
#include <bits/stdc++.h>
#define X first
#define Y second
#define MP make_pair
using namespace std;
const int MAXN = 1e5 + 12;
struct node{
bool trash = 0;
int t[2][2] = {{MAXN, MAXN}, {MAXN, MAXN}};
}t[MAXN * 4];
node merge(const node &x, const node &y){
if(x.trash)
return y;
else if(y.trash)
return x;
node tmp;
for(int i1 = 0;i1 < 2;i1++){
for(int j1 = 0;j1 < 2;j1++){
for(int i2 = 0;i2 < 2;i2++){
for(int j2 = 0;j2 < 2;j2++){
tmp.t[i1][j2] = min(tmp.t[i1][j2], x.t[i1][j1] + (j1 != i2) + y.t[i2][j2]);
}
}
}
}
return tmp;
}
int n, sz[MAXN], parent[MAXN], cl[MAXN];
int hldPtr, hldCnt, hld[MAXN], hldSt[MAXN], hldFin[MAXN], hldCmp[MAXN], hldId[MAXN];
vector< int > graph[MAXN];
pair< int, int > dp[MAXN];
void build(int v, int tl, int tr){
if(tl == tr){
t[v].t[0][0] = t[v].t[1][1] = 0;
return;
}
int tm = (tl + tr) / 2;
build(v * 2, tl, tm);
build(v * 2 + 1, tm + 1, tr);
t[v] = merge(t[v * 2], t[v * 2 + 1]);
}
void upd(int v, int tl, int tr, int pos){
if(tl > pos || pos > tr)
return;
if(tl == tr){
t[v].t[0][0] = t[v].t[1][1] = MAXN;
if(cl[hld[tl]] != 2)
t[v].t[0][0] = dp[hld[tl]].X;
if(cl[hld[tl]] != 1)
t[v].t[1][1] = dp[hld[tl]].Y;
return;
}
int tm = (tl + tr) / 2;
upd(v * 2, tl, tm, pos);
upd(v * 2 + 1, tm + 1, tr, pos);
t[v] = merge(t[v * 2], t[v * 2 + 1]);
}
node get(int v, int tl, int tr, int l, int r){
if(tl > r || l > tr)
return t[0];
if(tl >= l && tr <= r)
return t[v];
int tm = (tl + tr) / 2;
return merge(get(v * 2, tl, tm, l, r), get(v * 2 + 1, tm + 1, tr, l, r));
}
void dfs_sz(int v, int pr){
sz[v] = 1, parent[v] = pr;
for(int to: graph[v]){
if(to != pr){
dfs_sz(to, v);
sz[v] += sz[to];
}
}
}
void dfs(int v, int pr){
hldPtr++;
hld[hldPtr] = v, hldId[v] = hldPtr, hldCmp[v] = hldCnt;
if(hldSt[hldCnt] == 0)
hldSt[hldCnt] = v;
int mx = 0;
for(int to: graph[v]){
if(to != pr && sz[mx] < sz[to])
mx = to;
}
if(mx)
dfs(mx, v);
else
hldFin[hldCnt] = v;
for(int to: graph[v]){
if(to != pr && to != mx)
hldCnt++, dfs(to, v);
}
}
void initialize(int N, vector<int> A, vector<int> B) {
n = N, t[0].trash = 1;
for(int i = 0;i < n - 1;i++){
graph[A[i]].push_back(B[i]);
graph[B[i]].push_back(A[i]);
}
dfs_sz(1, -1);
dfs(1, 1);
build(1, 1, n);
}
int solve(int v, int _cl){
int tmpV = v;
while(v != -1){
int vSt = hldSt[hldCmp[v]], vFin = hldFin[hldCmp[v]];
node tmp = get(1, 1, n, hldId[vSt], hldId[vFin]);
if(vSt != 1){
dp[parent[vSt]].X -= min(min(tmp.t[0][0], tmp.t[0][1]), min(tmp.t[1][0], tmp.t[1][1]) + 1);
dp[parent[vSt]].Y -= min(min(tmp.t[0][0], tmp.t[0][1]) + 1, min(tmp.t[1][0], tmp.t[1][1]));
}
v = parent[vSt];
}
v = tmpV, cl[v] = _cl;
while(v != -1){
int vSt = hldSt[hldCmp[v]], vFin = hldFin[hldCmp[v]];
upd(1, 1, n, hldId[v]);
node tmp = get(1, 1, n, hldId[vSt], hldId[vFin]);
if(vSt != 1){
dp[parent[vSt]].X += min(min(tmp.t[0][0], tmp.t[0][1]), min(tmp.t[1][0], tmp.t[1][1]) + 1);
dp[parent[vSt]].Y += min(min(tmp.t[0][0], tmp.t[0][1]) + 1, min(tmp.t[1][0], tmp.t[1][1]));
}
else{
return min(min(tmp.t[0][0], tmp.t[0][1]), min(tmp.t[1][0], tmp.t[1][1]));
}
v = parent[vSt];
}
}
int cat(int v) {
return solve(v, 1);
}
int dog(int v) {
return solve(v, 2);
}
int neighbor(int v) {
return solve(v, 3);
}
