This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
vector<ll> adj[N];
vector<ll> subsiz(N), depth(N);
void dfs1(ll u, ll p){
subsiz[u] = 1;
trav(v,adj[u]){
if(v == p) conts;
depth[v] = depth[u]+1;
dfs1(v,u);
subsiz[u] += subsiz[v];
}
}
map<ll,ll> mp[N];
vector<ll> ans(N);
void dfs2(ll u, ll p){
pll best = {-1,-1};
trav(v,adj[u]){
if(v == p) conts;
pll px = {subsiz[v],v};
amax(best,px);
}
ll heavy = best.ss;
if(heavy == -1){
mp[u][subsiz[u]] = depth[u];
return;
}
dfs2(heavy,u);
swap(mp[u],mp[heavy]);
trav(v,adj[u]){
if(v == p or v == heavy) conts;
dfs2(v,u);
for(auto [x,d1] : mp[v]){
// x <= y
auto it = mp[u].lower_bound(x);
if(it != mp[u].end()){
auto [y,d2] = *it;
amax(ans[x],d1+d2-2*depth[u]);
}
// x > y
if(it != mp[u].begin()){
it--;
auto [y,d2] = *it;
amax(ans[y],d1+d2-2*depth[u]);
}
}
for(auto [x,d] : mp[v]){
auto it = mp[u].lower_bound(x);
if(it != mp[u].end() and it->second >= d) conts;
mp[u][x] = d;
it = mp[u].find(x);
vector<ll> torem;
while(it != mp[u].begin()){
it--;
if(it->second > d) break;
torem.pb(it->first);
}
trav(y,torem){
mp[u].erase(y);
}
}
}
{
ll x = subsiz[u], d = depth[u];
auto it = mp[u].lower_bound(x);
if(!(it != mp[u].end() and it->second >= d)){
mp[u][x] = d;
it = mp[u].find(x);
vector<ll> torem;
while(it != mp[u].begin()){
it--;
if(it->second > d) break;
torem.pb(it->first);
}
trav(y,torem){
mp[u].erase(y);
}
}
}
{
ll mx = subsiz[1]-subsiz[u];
auto it = mp[u].lower_bound(mx);
if(it != mp[u].end()){
auto [x,d] = *it;
amax(ans[mx],d-depth[u]+1);
}
}
}
vector<pll> ances;
void dfs3(ll u, ll p){
ances.pb({subsiz[1]-subsiz[u],u});
auto it = upper_bound(all(ances),make_pair(subsiz[u],-1ll));
if(it != ances.end()){
ll v = it->second;
amax(ans[subsiz[u]],depth[u]-depth[v]+1);
}
trav(v,adj[u]){
if(v == p) conts;
dfs3(v,u);
}
ances.pop_back();
}
void solve(int test_case)
{
ll n; cin >> n;
rep1(i,n-1){
ll u,v; cin >> u >> v;
adj[u].pb(v), adj[v].pb(u);
}
dfs1(1,-1);
dfs2(1,-1);
dfs3(1,-1);
rev(i,n,1) amax(ans[i],ans[i+1]);
rep1(i,n){
if(i&1) cout << 1 << endl;
else cout << ans[i/2]+1 << endl;
}
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
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