#include "bits/stdc++.h"
#include "catdog.h"
using i64 = long long;
#ifdef DEBUG
#include "/home/ahmetalp/Desktop/Workplace/debug.h"
#else
#define debug(...) void(23)
#endif
constexpr int inf = int(1E8);
using M = std::array<std::array<int, 2>, 2>;
M operator+ (const M& lhs, const M& rhs) {
M res;
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
res[i][j] = std::min({lhs[i][0] + rhs[0][j],
lhs[i][0] + rhs[1][j] + 1,
lhs[i][1] + rhs[0][j] + 1,
lhs[i][1] + rhs[1][j]});
}
}
return res;
}
constexpr int max_N = int(1E5);
#define def int mid = (l + r) >> 1, lv = v + 1, rv = v + ((mid - l) << 1)
struct segtree {
M tree[max_N << 1] {};
void build(int v, int l, int r) {
if (l + 1 == r) {
tree[v] = {0, inf, inf, 0};
debug(v, tree[v]);
return;
}
def;
build(lv, l, mid);
build(rv, mid, r);
tree[v] = tree[lv] + tree[rv];
}
void add(int v, int l, int r, int p, int x, int y) {
// assert(l <= p && p <= r);
if (l + 1 == r) {
tree[v][0][0] += x;
tree[v][1][1] += y;
return;
}
def;
if (p < mid) {
add(lv, l, mid, p, x, y);
} else {
add(rv, mid, r, p, x, y);
}
tree[v] = tree[lv] + tree[rv];
}
M get(int v, int l, int r, int ql, int qr) {
// assert(l <= ql && qr <= r);
if (ql == l && r == qr) {
return tree[v];
}
def;
if (qr <= mid) {
return get(lv, l, mid, ql, qr);
} else if (mid <= ql) {
return get(rv, mid, r, ql, qr);
} else {
return get(lv, l, mid, ql, mid)
+ get(rv, mid, r, mid, qr);
}
}
int v_cnt = 0;
int s_cnt = 0;
void add_size(int x) {
build(v_cnt, s_cnt, s_cnt + x);
v_cnt += (x << 1) - 1;
s_cnt += x;
}
} seg;
int N;
std::vector<int> adj[max_N];
int tim = 0;
int siz[max_N];
int par[max_N];
int top[max_N];
int tin[max_N];
int tout[max_N];
int len[max_N];
int typ[max_N];
int roots[max_N];
int ubl[max_N];
int ubr[max_N];
void dfs1(int v) {
siz[v] = 1;
for (auto& u : adj[v]) {
adj[u].erase(std::find(adj[u].begin(), adj[u].end(), v));
par[u] = v;
dfs1(u);
siz[v] += siz[u];
if (siz[u] > siz[adj[v][0]]) {
std::swap(u, adj[v][0]);
}
}
}
void dfs2(int v) {
tin[v] = tim++;
for (auto u : adj[v]) {
if (u == adj[v][0]) {
top[u] = top[v];
len[top[v]] += 1;
} else {
top[u] = u;
len[u] = 1;
}
dfs2(u);
}
tout[v] = tim;
if (v == top[v]) {
roots[v] = seg.v_cnt;
ubl[v] = seg.s_cnt;
ubr[v] = ubl[v] + len[v];
seg.add_size(len[v]);
}
}
void debug_tree() {
// auto dfs = [&](auto&& self, int v, int l, int r) -> void {
// if (l + 1 == r) {
// debug(l, r, seg.tree[v]);
// return;
// }
// def;
// self(self, lv, l, mid);
// self(self, rv, mid, r);
// };
// dfs(dfs, 0, 0, N);
// debug();
}
void initialize(int N, std::vector<int> A, std::vector<int> B) {
::N = N;
for (int i = 0; i < N - 1; ++i) {
--A[i], --B[i];
adj[A[i]].emplace_back(B[i]);
adj[B[i]].emplace_back(A[i]);
}
dfs1(0);
len[0] = 1;
dfs2(0);
debug(tin);
debug(len);
// debug_tree();
debug();
}
void rem(int u) {
std::vector<int> stk;
while (top[u]) {
u = top[u];
stk.emplace_back(u);
u = par[u];
}
std::reverse(stk.begin(), stk.end());
for (auto v : stk) {
M x = seg.get(roots[v], ubl[v], ubr[v], ubl[v], ubr[v]);
M y {};
int topp = top[par[v]];
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[par[v]] - tin[topp], -std::min({x[0][0], x[0][1], x[1][0] + 1, x[1][1] + 1}), -std::min({x[1][0], x[1][1], x[0][0] + 1, x[0][1] + 1}));
}
}
void add(int u) {
std::vector<int> stk;
while (top[u]) {
u = top[u];
stk.emplace_back(u);
u = par[u];
}
for (auto v : stk) {
M x = seg.get(roots[v], ubl[v], ubr[v], ubl[v], ubr[v]);
M y {};
int topp = top[par[v]];
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[par[v]] - tin[topp], std::min({x[0][0], x[0][1], x[1][0] + 1, x[1][1] + 1}), std::min({x[1][0], x[1][1], x[0][0] + 1, x[0][1] + 1}));
}
}
int answer() {
debug_tree();
M x = seg.get(roots[0], ubl[0], ubr[0], ubl[0], ubr[0]);
int res = inf;
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
res = std::min(res, x[i][j]);
}
}
return res;
}
int cat(int v) {
--v;
rem(v);
typ[v] = 1;
int topp = top[v];
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[v] - tin[topp], 0, inf);
add(v);
return answer();
}
int dog(int v) {
--v;
rem(v);
int topp = top[v];
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[v] - tin[topp], inf, 0);
add(v);
return answer();
}
int neighbor(int v) {
--v;
rem(v);
int topp = top[v];
if (typ[v] == 1) {
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[v] - tin[topp], 0, -inf);
} else {
seg.add(roots[topp], ubl[topp], ubr[topp], ubl[topp] + tin[v] - tin[topp], -inf, 0);
}
typ[v] = 0;
add(v);
return answer();
}
