A tree is an undirected graph with exactly one simple path between each pair of vertices. We call a set of simple paths k-valid if each vertex of the tree belongs to no more than one of these paths (including endpoints) and each path consists of exactly k vertices.

You are given a tree with n vertices. For each k from 1 to n inclusive find what is the maximum possible size of a k-valid set of simple paths.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of vertices in the tree.

Then following n - 1 lines describe the tree, each of them contains two integers v, u (1 ≤ v, u ≤ n) — endpoints of the corresponding edge.

It is guaranteed, that the given graph is a tree. 

Output

Output n numbers, the i-th of which is the maximum possible number of paths in an i-valid set of paths.

Examples

Input

7
1 2
2 3
3 4
4 5
5 6
6 7


Output

7
3
2
1
1
1
1



Input

6
1 2
2 3
2 4
1 5
5 6


Output

6
2
2
1
1
0

Note

One way to achieve the optimal number of paths for the second sample is illustrated in the following picture:

<image>
#include <bits/stdc++.h>
template <class c>
int popc(c a) {
  if (sizeof(c) == 8)
    return __builtin_popcountll(a);
  else
    return __builtin_popcount(a);
}
template <class c>
int ctz(c a) {
  if (sizeof(c) == 8)
    return __builtin_ctzll(a);
  else
    return __builtin_ctz(a);
}
template <class c>
int clz(c a) {
  if (sizeof(c) == 8)
    return __builtin_clzll(a);
  else
    return __builtin_clz(a);
}
inline int min(const int &first, const int &second) {
  return (((second - first) >> (32 - 1)) & (first ^ second)) ^ first;
}
inline int max(const int &first, const int &second) {
  return (((second - first) >> (32 - 1)) & (first ^ second)) ^ second;
}
inline long long min(const long long &first, const long long &second) {
  return (((second - first) >> (64 - 1)) & (first ^ second)) ^ first;
}
inline long long max(const long long &first, const long long &second) {
  return (((second - first) >> (64 - 1)) & (first ^ second)) ^ second;
}
using namespace std;
char string_in_buffer[(int)260];
void fast_scan(int &first) { scanf("%d", &first); }
void fast_scan(long long &first) { scanf("%lld", &first); }
void fast_scan(unsigned long long &first) { scanf("%llu", &first); }
void fast_scan(double &first) { scanf("%lf", &first); }
void fast_scan(long double &first) { scanf("%Lf", &first); }
void fast_scan(char &first) {
  scanf("%c", &first);
  if (first == '\n') {
    fast_scan(first);
  }
}
void fast_scan(string &first) {
  scanf("%s", string_in_buffer);
  first = string(string_in_buffer);
}
template <class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
  fast_scan(p.first);
  fast_scan(p.second);
}
template <class T>
void fast_scan(vector<T> &v) {
  for (auto &first : v) fast_scan(first);
}
void fast_print(const int &first) { printf("%d", first); }
void fast_print(const unsigned int &first) { printf("%u", first); }
void fast_print(const long long &first) { printf("%lld", first); }
void fast_print(const unsigned long long &first) { printf("%llu", first); }
void fast_print(const char &first) { printf("%c", first); };
void fast_print(const double &first) { printf("%.15lf", first); }
void fast_print(const long double &first) { printf("%.15Lf", first); }
void fast_print(const string &first) { printf("%s", first.c_str()); }
void fast_print(const char v[]) { fast_print((string)v); }
template <class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
  fast_print(p.first);
  fast_print(' ');
  fast_print(p.second);
}
template <class T>
void fast_print(const vector<T> &v) {
  if (v.empty()) return;
  fast_print(v[0]);
  for (int i = 1; i < v.size(); i++) {
    fast_print(' ');
    fast_print(v[i]);
  }
}
template <class T>
void fast_print(const vector<vector<T>> &v) {
  if (v.empty()) return;
  fast_print(v[0]);
  for (int i = 1; i < v.size(); i++) {
    fast_print('\n');
    fast_print(v[i]);
  }
}
template <class T>
void fast_print(const T &v) {
  for (const auto &first : v) {
    fast_print(first);
    fast_print(' ');
  }
}
using namespace std;
namespace smart_io {
string print_start = "";
string sep = " ";
bool first_print = false;
void precall_print() {
  fast_print(print_start);
  print_start = "\n";
  first_print = true;
}
void _print(deque<string>) {}
template <class T, class... Args>
void _print(deque<string> names, T elem, Args... args) {
  if (!first_print) {
    fast_print("\n");
  } else {
    first_print = false;
  }
  fast_print(names.front());
  fast_print(" = ");
  fast_print(elem);
  names.pop_front();
  _print(names, args...);
}
}  // namespace smart_io
template <class T>
ostream &operator,(ostream &os, const T &object) {
  if (!smart_io::first_print) {
    fast_print(smart_io::sep);
  } else {
    smart_io::first_print = false;
  }
  fast_print(object);
  return os;
}
template <class T>
istream &operator,(istream &is, T &object) {
  fast_scan(object);
  return is;
}
namespace escape__from__random__aetuhoetnuhshe {
using namespace std::chrono;
mt19937 rng(duration_cast<milliseconds>(system_clock::now().time_since_epoch())
                .count());
uniform_real_distribution<> prob_dist(0.0, 1.0);
};  // namespace escape__from__random__aetuhoetnuhshe
namespace typedefs {}
namespace numbers_operation {
template <class T>
inline T floor_mod(T a, const T &b) {
  a %= b;
  if (a < 0) a += b;
  return a;
}
}  // namespace numbers_operation
using namespace numbers_operation;
using namespace typedefs;
using namespace escape__from__random__aetuhoetnuhshe;
int n;
int Root = -1;
vector<vector<int>> h;
vector<int> it;
vector<int> g;
vector<int> max_path;
vector<int> tsize;
vector<int> only_path;
vector<pair<int, int>> jump;
void dfs0(int v, int _p) {
  max_path[v] = 1;
  tsize[v] = 1;
  for (int sub : h[v]) {
    if (sub == _p) continue;
    it[v]++;
    dfs0(sub, v);
    max_path[v] = max(max_path[v], max_path[sub] + 1);
    tsize[v] += tsize[sub];
  }
}
void dfs1(int v, int _p) {
  for (int sub : h[v]) {
    if (sub == _p) continue;
    g[--it[v]] = sub;
    dfs1(sub, v);
  }
}
void dfs2(int v, int _p) {
  vector<int> childs;
  for (int sub : h[v]) {
    if (sub == _p) continue;
    dfs2(sub, v);
    childs.push_back(sub);
  }
  if (((int)childs.size()) == 1) {
    jump[v] = make_pair(jump[childs[0]].first, jump[childs[0]].second + 1);
  } else {
    jump[v] = make_pair(v, 0);
  }
}
int paths = 0;
int dfs(int v, int k) {
  if (tsize[v] < k) return max_path[v];
  if (max_path[v] * 2 < k) return max_path[v];
  if (jump[v].first != v) {
    int t = dfs(jump[v].first, k) + jump[v].second;
    paths += t / k;
    t %= k;
    return t;
  }
  int m1 = 0, m2 = 0;
  for (int i = it[v]; i < it[v + 1]; i++) {
    int t = dfs(g[i], k);
    if (m1 < t) swap(m1, t);
    if (m2 < t) swap(m2, t);
  }
  if (m1 + m2 + 1 >= k) {
    paths++;
    return 0;
  } else
    return m1 + 1;
}
vector<int> mem;
int solve(int k) {
  if (k > n) return 0;
  if (mem[k] != -1) return mem[k];
  paths = 0;
  int t = dfs(Root, k);
  if (t >= k) paths++;
  return mem[k] = paths;
}
signed main(signed argc, char *argv[]) {
  cin, n;
  Root = rng() % n;
  mem.resize(n + 3, -1);
  it.resize(n + 1);
  h.resize(n);
  tsize.resize(n);
  max_path.resize(n);
  only_path.resize(n);
  jump.resize(n);
  for (int i = 0; i < (n - 1); i++) {
    int a, b;
    cin, a, b;
    a--, b--;
    h[a].push_back(b);
    h[b].push_back(a);
  }
  dfs0(Root, -1);
  for (int i = 1; i < n + 1; i++) {
    it[i] += it[i - 1];
  }
  g.resize(n - 1);
  dfs1(Root, -1);
  dfs2(Root, -1);
  vector<int> rez(n + 1);
  int cur = 1;
  while (cur <= n) {
    int cnt = solve(cur);
    if (cnt == 0) break;
    int l = cur;
    int r = n + 1;
    if (solve(cur + 1) == cnt) {
      while (r - l > 1) {
        int m = (l + r) / 2;
        if (solve(m) == cnt) {
          l = m;
        } else
          r = m;
      }
    }
    for (int j = cur; j <= l; j++) {
      rez[j] = cnt;
    }
    cur = l + 1;
  }
  for (int i = 1; i <= n; i++) {
    smart_io::precall_print();
    cout, rez[i];
  }
}
