#include "catdog.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int MAXN = 1e5;
const ll INF = 1e9;
vector <ll> adj[MAXN + 5];
ll sz[MAXN + 5], P[MAXN + 5], state[MAXN + 5], head[MAXN + 5];
ll MN[MAXN + 5], MX[MAXN + 5], tin[MAXN + 5], t;
void construct_chain(ll idx, ll par) {
tin[idx] = ++t;
MN[head[idx]] = min(MN[head[idx]], tin[idx]);
MX[head[idx]] = max(MX[head[idx]], tin[idx]);
for (auto i : adj[idx]) {
if (i != par) {
head[i] = (i == adj[idx][0] ? head[idx] : i);
construct_chain(i, idx);
}
}
}
void dfs(ll idx, ll par) {
sz[idx] = 1;
for (auto &i : adj[idx]) {
if (i != par) {
P[i] = idx;
dfs(i, idx);
sz[idx] += sz[i];
if (sz[i] > sz[adj[idx][0]]) {
swap(i, adj[idx][0]);
}
}
}
}
struct ST {
ll l, r;
ST *lf, *rg;
ll DP[2][2];
ST (ll _l, ll _r) {
l = _l, r = _r;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) DP[i][j] = INF;
}
}
void combine() {
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
DP[i][j] = INF;
for (int k = 0; k < 2; k++) {
for (int l = 0; l < 2; l++) {
DP[i][j] = min(DP[i][j], lf->DP[i][k] + rg->DP[l][j] + (k != l));
}
}
}
}
}
void build() {
if (l == r) {
DP[0][0] = DP[1][1] = 0;
return;
}
ll mid = (l + r) / 2;
lf = new ST(l, mid), rg = new ST(mid + 1, r);
lf->build(), rg->build();
combine();
}
void update(ll idx, pair<ll, ll> val) {
if (l == r) {
DP[0][0] += val.first;
DP[1][1] += val.second;
return;
}
ll mid = (l + r) / 2;
if (idx <= mid) lf->update(idx, val);
else rg->update(idx, val);
combine();
}
vector <vector<ll>> query(ll x, ll y) {
if (l > y || r < x) return {};
if (l >= x && r <= y) {
return {{DP[0][0], DP[0][1]}, {DP[1][0], DP[1][1]}};
}
vector <vector<ll>> L = lf->query(x, y), R = rg->query(x, y), ret(2, vector <ll> (2, INF));
if (L.empty()) return R;
if (R.empty()) return L;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 2; k++) {
for (int l = 0; l < 2; l++) {
ret[i][j] = min(ret[i][j], L[i][k] + R[l][j] + (k != l));
}
}
}
}
return ret;
}
} sg(1, 100000);
void initialize(int N, std::vector<int> A, std::vector<int> B) {
for (int i = 1; i <= N; i++) {
state[i] = -1;
MN[i] = INF, MX[i] = -INF;
}
for (int i = 0; i < N - 1; i++) {
adj[A[i]].push_back(B[i]);
adj[B[i]].push_back(A[i]);
}
dfs(1, -1);
head[1] = 1;
construct_chain(1, -1);
sg.build();
vector <ll> v;
for (int i = 1; i <= N; i++) {
if (head[i] == i) {
v.push_back(i);
}
}
sort(v.begin(), v.end(), [&](ll a, ll b) {
return tin[a] > tin[b];
});
for (auto i : v) {
vector <vector<ll>> cur = sg.query(MN[i], MX[i]);
if (P[i]) {
pair<ll, ll> val;
val.first = min({cur[0][0], cur[0][1], cur[1][0] + 1, cur[1][1] + 1});
val.second = min({cur[1][0], cur[1][1], cur[0][0] + 1, cur[0][1] + 1});
sg.update(tin[P[i]], val);
}
}
}
void solve(ll idx, ll d, ll c) {
ll D = d, C = c;
while (idx) {
vector <vector<ll>> cur = sg.query(MN[head[idx]], MX[head[idx]]);
pair<ll, ll> val, val2;
val.first = min({cur[0][0], cur[0][1], cur[1][0] + 1, cur[1][1] + 1});
val.second = min({cur[1][0], cur[1][1], cur[0][0] + 1, cur[0][1] + 1});
sg.update(tin[idx], {D, C});
cur = sg.query(MN[head[idx]], MX[head[idx]]);
val2.first = min({cur[0][0], cur[0][1], cur[1][0] + 1, cur[1][1] + 1});
val2.second = min({cur[1][0], cur[1][1], cur[0][0] + 1, cur[0][1] + 1});
D = val2.first - val.first;
C = val2.second - val.second;
idx = P[head[idx]];
}
}
int cat(int v) {
state[v] = 0;
solve(v, 0, INF);
vector <vector<ll>> cur = sg.query(MN[1], MX[1]);
return min({cur[0][0], cur[0][1], cur[1][0], cur[1][1]});
}
int dog(int v) {
state[v] = 1;
solve(v, INF, 0);
vector <vector<ll>> cur = sg.query(MN[1], MX[1]);
return min({cur[0][0], cur[0][1], cur[1][0], cur[1][1]});
}
int neighbor(int v) {
if (!state[v]) solve(v, 0, -INF);
else solve(v, -INF, 0);
state[v] = -1;
vector <vector<ll>> cur = sg.query(MN[1], MX[1]);
return min({cur[0][0], cur[0][1], cur[1][0], cur[1][1]});
}
