// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #include <x86intrin.h>
#include <bits/stdc++.h>
#include <chrono>
#include <random>
// @author: Vlapos
namespace operators
{
template <typename T1, typename T2>
std::istream &operator>>(std::istream &in, std::pair<T1, T2> &x)
{
in >> x.first >> x.second;
return in;
}
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &out, std::pair<T1, T2> x)
{
out << x.first << " " << x.second;
return out;
}
template <typename T1>
std::istream &operator>>(std::istream &in, std::vector<T1> &x)
{
for (auto &i : x)
in >> i;
return in;
}
template <typename T1>
std::ostream &operator<<(std::ostream &out, std::vector<T1> &x)
{
for (auto &i : x)
out << i << " ";
return out;
}
template <typename T1>
std::ostream &operator<<(std::ostream &out, std::set<T1> &x)
{
for (auto &i : x)
out << i << " ";
return out;
}
}
// name spaces
using namespace std;
using namespace operators;
// end of name spaces
// defines
#define ll long long
#define ull unsigned long long
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define pll pair<ll, ll>
#define f first
#define s second
#define uint unsigned int
#define all(vc) vc.begin(), vc.end()
// end of defines
// usefull stuff
void boost()
{
ios_base ::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
}
inline int getbit(int &x, int &bt) { return (x >> bt) & 1; }
const int dx4[4] = {-1, 0, 0, 1};
const int dy4[4] = {0, -1, 1, 0};
const int dx8[8] = {-1, -1, -1, 0, 0, 1, 1, 1};
const int dy8[8] = {-1, -0, 1, -1, 1, -1, 0, 1};
const ll INF = (1e18) + 500;
const int BIG = (1e9) * 2 + 100;
const int MAXN = (1e5) + 5;
const int MOD7 = (1e9) + 7;
const int MOD9 = (1e9) + 9;
const uint MODFFT = 998244353;
// #define int ll
struct test
{
vector<vector<int>> tree;
vector<int> answers, used;
int n;
int dfsC(int v, int szA, int pr = -1)
{
for (auto tov : tree[v])
if (!used[tov] and tov != pr and szA < sz[{tov, v}] * 2)
return dfsC(tov, szA, v);
return v;
}
map<pii, int> sz;
vector<vector<pii>> els;
vector<int> u, MX, SZ;
void dfsAdd(int v, int d, int pr, int RT, int A)
{
int P = min(sz[{v, pr}], A);
answers[P * 2] = max(answers[P * 2], d + 1);
els[RT].pb({sz[{v, pr}], d});
for (auto tov : tree[v])
if (tov != pr and !used[tov])
dfsAdd(tov, d + 1, v, RT, A);
}
void dfsSz(int v, int pr = -1)
{
SZ[v] = 1;
for (auto tov : tree[v])
if (tov != pr and !used[tov])
{
dfsSz(tov, v);
SZ[v] += SZ[tov];
}
}
void doSz(int v, int pr = -1)
{
int cSz = 1;
for (auto tov : tree[v])
if (tov != pr)
{
doSz(tov, v);
int toSz = sz[{tov, v}];
cSz += toSz;
sz[{v, tov}] = n - toSz;
}
if (pr != -1)
sz[{v, pr}] = cSz;
}
void getAns(int v)
{
dfsSz(v);
v = dfsC(v, SZ[v]);
used[v] = 1;
priority_queue<pii> cur;
set<pii> WTF;
int CNT = 0;
for (auto tov : tree[v])
if (!used[tov])
{
CNT++;
dfsAdd(tov, 1, v, tov, n - sz[{tov, v}]);
sort(all(els[tov]));
reverse(all(els[tov]));
cur.push({els[tov][0].f, tov});
WTF.insert({1, tov});
MX[tov] = -1;
}
if (CNT > 1)
{
while (cur.size())
{
pii bf = cur.top();
cur.pop();
auto [sz, rt] = bf;
int cMx = WTF.begin()->s == rt ? next(WTF.begin())->f : WTF.begin()->f;
cMx = -cMx;
if (cMx != -1 and sz * 2 <= n)
{
answers[sz * 2] = max(answers[sz * 2], cMx + 1 + els[rt][u[rt]].s);
}
WTF.erase({-MX[rt], rt});
MX[rt] = max(MX[rt], els[rt][u[rt]].s);
WTF.insert({-MX[rt], rt});
u[bf.s]++;
if (els[bf.s].size() > u[bf.s])
cur.push({els[bf.s][u[bf.s]].f, bf.s});
}
}
for (auto tov : tree[v])
if (!used[tov])
{
u[tov] = 0;
els[tov].clear();
els[tov].shrink_to_fit();
}
for (auto tov : tree[v])
if (!used[tov])
getAns(tov);
}
void solve(int testcase)
{
boost();
cin >> n;
used.resize(n);
tree.resize(n);
SZ.resize(n);
answers.resize(n + 1);
if (2 <= n)
answers[2] = 2;
MX.resize(n);
els.resize(n);
u.resize(n);
for (int i = 0; i < n - 1; ++i)
{
int v, tov;
cin >> v >> tov;
--v, --tov;
tree[v].pb(tov);
tree[tov].pb(v);
}
doSz(0, -1);
getAns(0);
for (int i = (n / 2) * 2 - 2; i > 0; i -= 2)
{
answers[i] = max(answers[i], answers[i + 2]);
}
for (int i = 1; i <= n; ++i)
{
int cur = max(1, answers[i]);
cout << cur << "\n";
}
}
};
main()
{
boost();
int q = 1;
// cin >> q;
for (int i = 0; i < q; i++)
{
test t;
t.solve(i);
}
return 0;
}
//[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]//
// //
// Coded by Der_Vlἀpos //
// //
//[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]//
