#include <bits/stdc++.h>
using namespace std;
#define ii pair<int, int>
#define fi first
#define se second
// #define int long long
#define ll long long
#define ld double
#define mp make_pair
#define lg2 30
#define iii pair<int, ii>
#define iiii pair<ii, ii>
#define base 29
#define eps 1e-8
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
int dx[] = {0LL, 0LL, 1, -1, 1, 1, -1, -1};
int dy[] = {1, -1, 0LL, 0LL, 1, -1, 1, -1};
const int maxn = 4e5 + 5;
const int mod = 1e9 + 7;
int n, dp[maxn][3], tt[maxn], sz[maxn], head[maxn], pos[maxn], siz[maxn], par[maxn];
vector<int> a[maxn];
void prepare(int u, int cha)
{
sz[u] = 1;
for (int v : a[u])
{
if (v == cha)
continue;
par[v] = u;
sz[u] += sz[v];
prepare(v, u);
}
}
void hld(int u, int dau, int cha)
{
cout << u << " " << dau << '\n';
head[u] = dau;
pos[u] = ++siz[dau];
int bigchild = 0;
for (int v : a[u])
{
if (v == cha)
continue;
if (sz[bigchild] < sz[v])
{
bigchild = v;
}
}
if (bigchild)
hld(bigchild, dau, u);
for (int v : a[u])
{
if (v != bigchild && v != cha)
{
hld(v, v, u);
}
}
}
struct node
{
int x[2][2];
node()
{
for (int i = 0; i <= 1; i++)
{
for (int j = 0; j <= 1; j++)
{
x[i][j] = n;
}
}
}
};
struct segmentree
{
vector<node> tree;
void init(int _n)
{
tree.resize(4 * _n + 5);
}
node Merge(node &a, node &b)
{
node ans;
for (int i = 0; i <= 1; i++)
{
for (int j = 0; j <= 1; j++)
{
for (int x = 0; x <= 1; x++)
{
for (int y = 0; y <= 1; y++)
{
ans.x[i][y] = min(ans.x[i][y], a.x[i][j] + b.x[x][y] + (j != x));
}
}
}
}
return ans;
}
void build(int id, int l, int r)
{
if (l == r)
{
tree[id].x[1][1] = tree[id].x[0][0] = 0;
return;
}
int mid = (l + r) / 2;
build(id * 2, l, mid);
build(id * 2 + 1, mid + 1, r);
tree[id] = Merge(tree[id * 2], tree[id * 2 + 1]);
}
void update(int id, int l, int r, int i, int cat, int dog)
{
if (l == r)
{
tree[id].x[0][0] += cat;
tree[id].x[1][1] += dog;
return;
}
int mid = (l + r) / 2;
if (i <= mid)
update(id * 2, l, mid, i, cat, dog);
else
update(id * 2 + 1, mid + 1, r, i, cat, dog);
tree[id] = Merge(tree[id * 2], tree[id * 2 + 1]);
}
node get()
{
return tree[1];
}
} st[maxn];
void update(int u, int cat, int dog)
{
while (u)
{
node trc = st[head[u]].get();
int trc_cat = min({trc.x[0][0], trc.x[0][1], trc.x[1][0] + 1, trc.x[1][1] + 1});
int trc_dog = min({trc.x[1][1], trc.x[1][0], trc.x[0][1] + 1, trc.x[0][0] + 1});
st[head[u]].update(1, 1, siz[head[u]], pos[u], cat, dog);
trc = st[head[u]].get();
int ht_cat = min({trc.x[0][0], trc.x[0][1], trc.x[1][0] + 1, trc.x[1][1] + 1});
int ht_dog = min({trc.x[1][1], trc.x[1][0], trc.x[0][1] + 1, trc.x[0][0] + 1});
cat = ht_cat - trc_cat;
dog = ht_dog - trc_dog;
u = par[head[u]];
}
}
int getans()
{
return min({st[1].tree[1].x[0][1], st[1].tree[1].x[1][0], st[1].tree[1].x[1][1], st[1].tree[1].x[0][0]});
}
int cat(int v)
{
tt[v] = 1;
update(v, 0, n);
return getans();
}
int dog(int v)
{
tt[v] = 2;
update(v, n, 0);
return getans();
}
int neighbor(int v)
{
if (tt[v] == 1)
{
update(v, 0, -n);
}
else
update(v, -n, 0);
tt[v] = 0;
return getans();
}
void initialize(int N, vector<int> A, vector<int> B)
{
n = N;
for (int i = 0; i < n - 1; i++)
{
a[A[i]].push_back(B[i]);
a[B[i]].push_back(A[i]);
}
prepare(1, -1);
hld(1, 1, -1);
for (int i = 1; i <= n; i++)
{
if (head[i] == i)
{
st[i].init(siz[i]);
st[i].build(1, 1, siz[i]);
}
}
}
/*signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define task "task"
if (fopen(task ".inp", "r"))
{
freopen(task ".inp", "r", stdin);
freopen(task ".out", "w", stdout);
}
initialize(3, {1, 2, 2, 4}, {2, 3, 4, 5});
cout << cat(3) << " ";
cout << dog(5) << " ";
cout << cat(2) << " ";
cout << dog(1);
cerr << endl
<< "TIME : " << clock() * 0.001 << "s" << endl;
}*/
