#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define eb emplace_back
#define pu push
#define ins insert
#define fi first
#define se second
#define all(a) a.begin(),a.end()
#define bruh ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fu(x,a,b) for (auto x=a;x<=b;x++)
#define fd(x,a,b) for (auto x=a;x>=b;x--)
#define int ll
using namespace std;
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
/*
Competitive Programming notes that I need to study & fix my dumbass self:
1. Coding:
- Always be sure to check the memory of arrays (maybe use vectors), for loops
- Always try to maximize the memory if possible, even if you are going for subtasks
- Do not exploit #define int long long, it will kill you
2. Stress:
- Always try generating big testcases and try if they run
3. Time management:
- Don't overcommit or undercommit, always spend a certain amount of time to think a problem, don't just look at it and say I'm fucked
- Do not spend too much time coding brute-force solutions, they should be easily-codable solutions that don't take up too much time
Time management schedule:
Offline / LAH days (4 problems - 3h):
15' thinking of solution / idea
1. no idea: skip
2. yes idea: continue thinking for <= 15'
+ implementing: <= 20'
+ brute-force: <= 5'
+ test generator: <= 5'
I hate offline because I am dumb
*/
typedef pair<int, int> ii;
const int N = 1e5+5;
const int B = 750;
const int mod = 1e9+7;
const int inf = 1e9;
using cd = complex<double>;
const long double PI = acos(-1);
int power(int a,int b) {ll x = 1;if (a >= mod) a%=mod; while (b) {if (b & 1) x = x*a % mod;a = a*a % mod;b>>=1;}return x;}
struct Matrix {
int a[2][2];
Matrix() {
a[0][0] = a[1][1] = 0;
a[0][1] = a[1][0] = inf;
}
static Matrix cat()
{
Matrix a;
a.a[1][1] = inf;
return a;
}
static Matrix dog()
{
Matrix a;
a.a[0][0] = inf;
return a;
}
static Matrix rcat()
{
Matrix a;
a.a[1][1] = -inf;
return a;
}
static Matrix rdog()
{
Matrix a;
a.a[0][0] = -inf;
return a;
}
};
Matrix merge(const Matrix &a, const Matrix &b) {
Matrix c;
for (int i=0;i<2;i++) for (int v=0;v<2;v++) c.a[i][v] = inf;
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
if (a.a[i][j] >= inf) continue;
for (int u = 0; u < 2; ++u) {
for (int v = 0; v < 2; ++v) {
if (b.a[u][v] >= inf) continue;
c.a[i][v] = min(c.a[i][v], a.a[i][j] + b.a[u][v] + (j != u));
}
}
}
}
return c;
}
struct Segtree {
int n;
vector<Matrix> st;
void init(int _)
{
n = _;
st.assign(4*_ + 5, Matrix());
}
void Set(int id, int l, int r, int i, int tp)
{
if (l == r)
{
if (tp == 0) st[id] = Matrix();
else if (tp == 1) st[id] = Matrix::cat();
else st[id] = Matrix::dog();
return;
}
int mid = l+r>>1;
if (i <= mid) Set(id*2, l, mid, i, tp);
else Set(id*2+1, mid+1, r, i, tp);
st[id] = merge(st[id*2], st[id*2+1]);
}
void update(int id, int l, int r, int i, ii a)
{
if (l == r)
{
st[id].a[0][0] += a.fi, st[id].a[1][1] += a.se;
return;
}
int mid = l+r>>1;
if (i <= mid) update(id*2, l, mid, i, a);
else update(id*2+1, mid+1, r, i, a);
st[id] = merge(st[id*2], st[id*2+1]);
}
void upd(int i, ii v)
{
update(1, 1, n, i, v);
}
void set(int i, int tp)
{
Set(1, 1, n, i, tp);
}
} st[N];
int n;
vector<int> adj[N];
int val[N];
int sz[N], par[N], heavy[N], head[N], len[N];
int tin[N], tout[N], timer = 0;
void reset()
{
timer = 0;
for (int i = 1; i <= n; i++)
{
val[i] = -1;
sz[i] = par[i] = heavy[i] = head[i] = tin[i] = tout[i] = 0;
adj[i].clear();
}
}
void predfs(int u, int p)
{
sz[u] = 1;
par[u] = p;
for (auto v : adj[u])
{
if (v == p) continue;
predfs(v, u);
sz[u] += sz[v];
if (sz[v] > sz[heavy[u]]) heavy[u] = v;
}
}
void decompose(int u, int p)
{
len[p]++;
head[u] = p;
tin[u] = ++timer;
if (heavy[u]) decompose(heavy[u], p);
for (auto v : adj[u])
{
if (v == par[u] || v == heavy[u]) continue;
decompose(v, v);
}
tout[u] = timer;
}
int id(int u)
{
return tin[u] - tin[head[u]] + 1;
}
ii delta(Matrix prv, Matrix cur)
{
ii c, p;
c.fi = min({cur.a[0][0], cur.a[0][1], cur.a[1][1] + 1, cur.a[1][0] + 1});
c.se = min({cur.a[1][0], cur.a[1][1], cur.a[0][0] + 1, cur.a[0][1] + 1});
p.fi = min({prv.a[0][0], prv.a[0][1], prv.a[1][1] + 1, prv.a[1][0] + 1});
p.se = min({prv.a[1][0], prv.a[1][1], prv.a[0][0] + 1, prv.a[0][1] + 1});
return {c.fi - p.fi, c.se - p.se};
}
void del(int u)
{
Matrix prv = st[head[u]].st[1];
if (val[u] == 1) st[head[u]].upd(id(u), {0, -inf});
else st[head[u]].upd(id(u), {-inf, 0});
Matrix cur = st[head[u]].st[1];
while (true)
{
u = head[u];
if (!par[u]) break;
Matrix pprv = st[head[par[u]]].st[1];
st[head[par[u]]].upd(id(par[u]), delta(prv, cur));
prv = pprv; cur = st[head[par[u]]].st[1];
u = par[u];
}
}
void add(int u)
{
Matrix prv = st[head[u]].st[1];
if (val[u] == 1) st[head[u]].upd(id(u), {0, inf});
else st[head[u]].upd(id(u), {inf, 0});
Matrix cur = st[head[u]].st[1];
while (true)
{
u = head[u];
if (!par[u]) break;
Matrix pprv = st[head[par[u]]].st[1];
st[head[par[u]]].upd(id(par[u]), delta(prv, cur));
prv = pprv, cur = st[head[par[u]]].st[1];
u = par[u];
}
}
int cat(int u)
{
assert(val[u] == -1);
val[u] = 1;
add(u);
Matrix res = st[1].st[1];
return min({res.a[0][0], res.a[0][1], res.a[1][0], res.a[1][1]});
}
int dog(int u)
{
assert(val[u] == -1);
val[u] = 2;
add(u);
Matrix res = st[1].st[1];
return min({res.a[0][0], res.a[0][1], res.a[1][0], res.a[1][1]});
}
int neighbor(int u)
{
assert(val[u] != -1);
del(u);
val[u] = -1;
Matrix res = st[1].st[1];
return min({res.a[0][0], res.a[0][1], res.a[1][0], res.a[1][1]});
}
void initialize(int _, vector<int> A, vector<int> B) {
n = _;
reset();
for (int i = 0; i < n-1; i++)
{
adj[A[i]].pb(B[i]); adj[B[i]].pb(A[i]);
}
predfs(1, 0);
decompose(1, 1);
// for (int i = 1; i <= n; i++) cout<<head[i]<<" ";
// cout<<endl;
for (int i = 1; i <= n; i++)
{
if (head[i] == i)
{
st[i].init(len[i]);
}
}
}
/*
Go through the mistakes you usually make and revise your code, for god's sake...
*/
// signed main()
// {
// bruh
// int n = 5;
// vector<int> A = {1, 2, 2, 4};
// vector<int> B = {2, 3, 4, 5};
// initialize(n, A, B);
// cout<<cat(3)<<endl;
// cout<<dog(5)<<endl;
// cout<<cat(2)<<endl;
// cout<<dog(1)<<endl;
// cout<<neighbor(2)<<endl;
// }
