#include "catdog.h"
#include <bits/stdc++.h>
#define int ll
using namespace std;
#define ll long long
#define y1 zck_is_king
#define pii pair<ll, ll>
#define ull unsigned ll
#define f first
#define s second
#define ALL(x) x.begin(),x.end()
#define SZ(x) (int)x.size()
#define SQ(x) (x)*(x)
#define MN(a,b) a = min(a,(__typeof__(a))(b))
#define MX(a,b) a = max(a,(__typeof__(a))(b))
#define pb push_back
#define REP(i,n) for (int i = 0; i<n; ++i)
#define RREP(i,n) for (int i = n-1; i>=0; --i)
#define REP1(i,n) for (int i = 1; i<=n; ++i)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#ifdef BALBIT
#define IOS()
#define bug(...) fprintf(stderr,"#%d (%s) = ",__LINE__,#__VA_ARGS__),_do(__VA_ARGS__);
template<typename T> void _do(T &&x){cerr<<x<<endl<<flush;}
template<typename T, typename ...S> void _do(T &&x, S &&...y){cerr<<x<<", ";_do(y...);}
#else
#define IOS() ios_base::sync_with_stdio(0);cin.tie(0);
#define endl '\n'
#define bug(...)
#endif
const int iinf = 1e9+10;
const ll inf = 1ll<<29;
const ll mod = 1e9+7 ;
void GG(){cout<<"0\n"; exit(0);}
ll mpow(ll a, ll n, ll mo = mod){ // a^n % mod
ll re=1;
while (n>0){
if (n&1) re = re*a %mo;
a = a*a %mo;
n>>=1;
}
return re;
}
ll inv (ll b, ll mo = mod){
if (b==1) return b;
return (mo-mo/b) * inv(mo%b,mo) % mo;
}
const int maxn = 1e5+5;
struct segtree{
// segtree for this chain
int MAXN;
vector<array<array<int,2>, 2> > s; // s[o][a][b]: from type a (higher) to type b (lower) 0 is cat, 1 is dog
void MO(int p, int n0, int n1, int o, int l, int r) {
if (l > p || r < p) return;
if (l == r) {
s[o][0][0]=n0;
s[o][1][1]=n1;
s[o][0][1]=inf;
s[o][1][0]=inf;
return;
}
int mid = (l+r)/2;
MO(p,n0,n1,o*2,l,mid);
MO(p,n0,n1,o*2+1,mid+1,r);
REP(i,2) REP(j,2) {
s[o][i][j] = inf;
REP(a,2) REP(b,2){
MN(s[o][i][j], s[o*2][i][a] + s[o*2+1][b][j] + (a!=b));
}
}
}
void MO(int p, int n0, int n1) {
MO(p,n0,n1,1,0,MAXN-1);
}
array<int, 2> get(){
array<int, 2> re = {{inf, inf}};
REP(t,2) REP(i,2) REP(j,2) {
MN(re[t], s[1][i][j] + (i!=t));
}
return re;
}
int gans(){
int re = inf;
REP(i,2) REP(j,2) {
// bug(i,j,s[1][i][j]);
MN(re, s[1][i][j]);
}
return re;
}
segtree(){}
void init(int ss){
MAXN = ss;
s.resize(ss*4, {{{{inf,inf}}, {{inf, inf}}}});
}
};
//int treeidx[maxn]; // position on chain, with 0 being the head
int head[maxn]; // head of each node
int sz[maxn], par[maxn];
vector<int> g[maxn];
int catdog[maxn], dep[maxn]; // -1:nothing, 0:cat, 1:dog
int ifcat[maxn], ifdog[maxn]; // cost of being cat or dog
void dfs(int v, int p) {
sz[v] = 1;
for (int u : g[v]) {
if (u != p) {
par[u] = v;
dep[u] = dep[v] + 1;
dfs(u,v);
sz[v] += sz[u];
}
}
}
int chainsize[maxn];
void dfs2(int v, int p) {
chainsize[head[v]]++;
int mx = 0, mxc = -1;
for (int u : g[v]) {
if (u!=p) {
if (sz[u] > mx) {
mx = sz[u]; mxc = u;
}
}
}
for (int u : g[v]) {
if (u !=p) {
if (u == mxc) {
head[u] = head[v];
}else{
head[u] = u;
}
dfs2(u,v);
}
}
}
segtree TT[maxn]; // for each head
void upd(int v) {
// update a node
if (catdog[v] == -1) {
// no animal
TT[head[v]].MO(dep[v] - dep[head[v]], ifcat[v], ifdog[v]);
}else if (catdog[v] == 0) {
bug("hello/");
TT[head[v]].MO(dep[v] - dep[head[v]], ifcat[v], inf);
// cat
}else{
// doge
bug("hello/ dog");
TT[head[v]].MO(dep[v] - dep[head[v]], inf, ifdog[v]);
}
}
void chainupd(int v) {
while (1) {
array<int, 2> old = TT[head[v]].get();
upd(v);
if (head[v] == 0) break;
array<int, 2> yo = TT[head[v]].get();
int nxt = par[head[v]];
ifcat[nxt] += yo[0] - old[0];
ifdog[nxt] += yo[1] - old[1];
v = nxt;
}
}
void initialize(signed n, vector<signed> a, vector<signed> b) {
REP(i,n-1) {
g[a[i]-1].pb(b[i]-1);
g[b[i]-1].pb(a[i]-1);
}
dfs(0, -1);
dfs2(0,-1);
REP(i,n) {
bug(i, head[i], chainsize[head[i]]);
if (head[i] == i) {
TT[i].init(chainsize[i]);
}
}
REP(i,n) catdog[i] = -1;
REP(i,n) {
upd(i);
}
}
signed yar(signed v, signed nw) {
--v;
catdog[v] = nw;
chainupd(v);
// array<int, 2> ho = TT[0].get();
int ret = TT[0].gans();
bug(ret);
return ret;
}
signed cat(signed v) {
return yar(v,0);
}
signed dog(signed v) {
return yar(v,1);
}
signed neighbor(signed v) {
return yar(v,-1);
}
/*
5
1 2
2 3
2 4
1 5
7
*/
