Problem: Let G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v ∈ W the distance between u and v is either k or k+1.

You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.

Input

The first line contains a single integer n (2 ≤ n ≤ 5 ⋅ 10^5) – the number of vertices of the tree.

Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 ≤ u_i, v_i ≤ n) meaning that there is an edge between vertices u_i and v_i. 

It is guaranteed that the given graph is tree. 

Output

Output a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.

Examples

Input


5
1 2
1 3
1 4
4 5


Output


4 3 2 1 1


Input


6
1 2
1 3
1 4
4 5
4 6


Output


4 4 2 1 1 1

Note

Consider the first example. 

  * The only maximum almost-1-uniform set is \{1, 2, 3, 4\}. 
  * One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}. 
  * A maximum almost-3-uniform set is any pair of vertices on distance 3. 
  * Any single vertex is an almost-k-uniform set for k ≥ 1. 



In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
vector<vector<int>> g;
vector<int> down;
vector<int> order;
vector<int> pv;
void Dfs(int v) {
  order.push_back(v);
  down[v] = 0;
  for (int u : g[v]) {
    if (u == pv[v]) {
      continue;
    }
    pv[u] = v;
    Dfs(u);
    down[v] = max(down[v], down[u] + 1);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  g.resize(n);
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    --x;
    --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  down.resize(n);
  order.clear();
  pv.resize(n);
  pv[0] = -1;
  Dfs(0);
  vector<int> ans(n + 1, 1);
  vector<int> up(n, 0);
  vector<int> children;
  vector<int> cc;
  vector<vector<int>> vcc(n);
  for (int it = 0; it < (int)order.size(); it++) {
    children.clear();
    cc.clear();
    int v = order[it];
    for (int u : g[v]) {
      if (u == pv[v]) {
        continue;
      }
      children.push_back(u);
      cc.push_back(down[u] + 1);
    }
    cc.push_back(up[v]);
    if (up[v] != 0) {
      cc.push_back(0);
    }
    sort(cc.rbegin(), cc.rend());
    int sz = (int)cc.size();
    for (int i = 1; i < sz - 1; i++) {
      ans[2 * cc[i] - 1] = max(ans[2 * cc[i] - 1], i + 1);
    }
    for (int i = 1; i < sz; i++) {
      if (cc[i] < cc[i - 1]) {
        ans[2 * cc[i] + 1] = max(ans[2 * cc[i] + 1], i + 1);
      }
    }
    for (int i = 1; i < sz - 1; i++) {
      ans[2 * cc[i]] = max(ans[2 * cc[i]], i + 1);
    }
    if (pv[v] != -1) {
      int id_up = 0;
      while (cc[id_up] != up[v]) {
        ++id_up;
      }
      int first = -1;
      int second = -1;
      for (int i = 0; i < sz; i++) {
        if (i == id_up) {
          continue;
        }
        if (first == -1) {
          first = cc[i];
        } else {
          second = cc[i];
          break;
        }
      }
      int ptr = 0;
      for (int h = second; h >= 1; h--) {
        while (ptr < sz && cc[ptr] >= h) {
          ++ptr;
        }
        int realz = ptr - (id_up < ptr);
        auto iter = lower_bound(vcc[pv[v]].begin(), vcc[pv[v]].end(), h);
        realz += (int)(vcc[pv[v]].end() - iter) - 1;
        ans[2 * h] = max(ans[2 * h], realz);
      }
    }
    vcc[v] = cc;
    reverse(vcc[v].begin(), vcc[v].end());
    for (int u : children) {
      if (cc[0] == down[u] + 1) {
        up[u] = cc[1] + 1;
      } else {
        up[u] = cc[0] + 1;
      }
    }
  }
  for (int i = n; i >= 3; i--) {
    ans[i - 2] = max(ans[i - 2], ans[i]);
  }
  for (int i = 1; i <= n; i++) {
    if (i > 1) {
      cout << " ";
    }
    cout << ans[i];
  }
  cout << '\n';
  return 0;
}