// 15:59
#include "bits/stdc++.h"
#include "catdog.h"
#ifdef DEBUG
#include "/home/ahmetalp/Desktop/Workplace/debug.h"
#else
#define debug(...) void(23)
#endif
using i64 = long long;
constexpr i64 inf = i64(1E9);
using M = std::array<std::array<i64, 2>, 2>;
M operator+ (M lhs, 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;
}
#define def int mid = (l + r) >> 1, lv = v + 1, rv = v + ((mid - l + 1) << 1)
struct segtree {
int n;
std::vector<M> tree;
segtree() {}
segtree(int n_) : n(n_), tree(n << 1) {
auto dfs = [&](auto&& self, int v, int l, int r) -> void {
if (l == r) {
tree[v] = {0, inf, inf, 0};
return;
}
def;
self(self, lv, l, mid);
self(self, rv, mid + 1, r);
tree[v] = tree[lv] + tree[rv];
};
dfs(dfs, 0, 0, n - 1);
}
void init(int n_) {
n = n_;
tree.assign(n << 1, {});
auto dfs = [&](auto&& self, int v, int l, int r) -> void {
if (l == r) {
tree[v] = {0, inf, inf, 0};
return;
}
def;
self(self, lv, l, mid);
self(self, rv, mid + 1, r);
tree[v] = tree[lv] + tree[rv];
};
dfs(dfs, 0, 0, n - 1);
}
void modify(int v, int l, int r, int p, int k, i64 x) {
if (l == r) {
tree[v][k >> 1][k & 1] += x;
return;
}
def;
if (p <= mid) {
modify(lv, l, mid, p, k, x);
} else {
modify(rv, mid + 1, r, p, k, x);
}
tree[v] = tree[lv] + tree[rv];
}
void modify(int p, int k, i64 x) {
modify(0, 0, n - 1, p, k, x);
}
M get(int v, int l, int r, int ql, int qr) {
if (ql == l && r == qr) {
return tree[v];
}
def;
if (qr <= mid) {
return get(lv, l, mid, ql, qr);
} else if (mid + 1 <= ql) {
return get(rv, mid + 1, r, ql, qr);
} else {
return get(lv, l, mid, ql, mid)
+ get(rv, mid + 1, r, mid + 1, qr);
}
}
M get(int l, int r) {
return get(0, 0, n - 1, l, r);
}
} seg;
int tim;
std::vector<int> tp;
std::vector<int> siz, par, top, tin, len;
std::vector<std::vector<int>> adj;
void dfs1(int v) {
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(adj[v][0], u);
}
}
}
void dfs2(int v) {
len[top[v]]++;
tin[v] = tim++;
for (auto& u : adj[v]) {
top[u] = (u == adj[v][0] ? top[v] : u);
dfs2(u);
}
}
void initialize(int N, std::vector<int> A, std::vector<int> B) {
tp.assign(N, 0);
siz.assign(N, 1);
par.assign(N, 0);
top.assign(N, {});
tin.assign(N, 0);
len.assign(N, 0);
adj.assign(N, {});
seg.init(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]);
}
debug(0);
dfs1(0);
debug(1);
dfs2(0);
debug(2);
}
void add(int v, int t) {
debug("add", v, t);
int u = v;
while (top[u] != 0) {
if (u == top[u]) {
M x = seg.get(tin[u], tin[u] + len[u] - 1);
debug(x);
seg.modify(tin[par[u]], 0, t * std::min({x[0][0], x[0][1], x[1][0] + 1, x[1][1] + 1}));
seg.modify(tin[par[u]], 3, t * std::min({x[0][0] + 1, x[0][1] + 1, x[1][0], x[1][1]}));
u = par[u];
} else {
u = top[u];
}
}
}
int answer() {
M res = seg.get(0, len[0] - 1);
debug("answer", res);
i64 ans = inf;
for (int i = 0; i < 4; ++i) {
ans = std::min(ans, res[i >> 1][i & 1]);
}
return ans;
}
int cat(int v) {
debug("cat", v);
--v;
add(v, -1);
tp[v] = 1;
seg.modify(tin[v], 3, inf);
add(v, +1);
return answer();
}
int dog(int v) {
debug("dog", v);
--v;
add(v, -1);
tp[v] = 2;
seg.modify(tin[v], 0, inf);
add(v, +1);
return answer();
}
int neighbor(int v) {
debug("neighbor", v);
--v;
add(v, -1);
if (tp[v] == 1) {
seg.modify(tin[v], 3, -inf);
} else if (tp[v] == 2) {
seg.modify(tin[v], 0, -inf);
} else {
assert(false);
}
tp[v] = 0;
add(v, +1);
return answer();
}
