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>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
using namespace std;
namespace {
namespace shik {
template <class T>
void _R(T &x) {
  cin >> x;
}
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%" SCNd64, &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template <class T, class... U>
void R(T &head, U &...tail) {
  _R(head);
  R(tail...);
}
template <class T>
void _W(const T &x) {
  cout << x;
}
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%" PRId64, x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template <class T>
void _W(const vector<T> &x) {
  for (auto i = x.begin(); i != x.end(); _W(*i++))
    if (i != x.cbegin()) putchar(' ');
}
void W() {}
template <class T, class... U>
void W(const T &head, const U &...tail) {
  _W(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  W(tail...);
}
template <class T, class F = less<T>>
void sort_uniq(vector<T> &v, F f = F()) {
  sort(begin(v), end(v), f);
  v.resize(unique(begin(v), end(v)) - begin(v));
}
template <class T>
inline T bit(T x, int i) {
  return (x >> i) & 1;
}
template <class T>
inline bool chkmax(T &a, const T &b) {
  return b > a ? a = b, true : false;
}
template <class T>
inline bool chkmin(T &a, const T &b) {
  return b < a ? a = b, true : false;
}
template <class T>
using MaxHeap = priority_queue<T>;
template <class T>
using MinHeap = priority_queue<T, vector<T>, greater<T>>;
const int N = 1e5 + 10;
int n, k;
vector<int> e[N];
void make_tree(int p) {
  for (int i : e[p]) {
    e[i].erase(find(begin(e[i]), end(e[i]), p));
    make_tree(i);
  }
}
pair<int, int> go(int p) {
  int s = 0, r = 0, a1 = 0, a2 = 0;
  for (int i : e[p]) {
    auto t = go(i);
    s += t.first;
    int x = t.second;
    if (x >= a1) {
      a2 = a1;
      a1 = x;
    } else if (x >= a2) {
      a2 = x;
    }
  }
  if (a1 + a2 + 1 >= k) {
    s++;
  } else {
    r = a1 + 1;
  }
  return {s, r};
}
int shik(int _k) {
  k = _k;
  return go(1).first;
}
int ans[N];
void solve(int l, int r, int al, int ar) {
  if (r - l <= 1) return;
  if (al == ar) {
    for (int i = (l); i <= int(r); i++) ans[i] = al;
    return;
  }
  int m = (l + r) / 2;
  int am = shik(m);
  ans[m] = am;
  solve(l, m, al, am);
  solve(m, r, am, ar);
}
void main() {
  R(n);
  for (int i = 0; i < int(n - 1); i++) {
    int a, b;
    R(a, b);
    e[a].push_back(b);
    e[b].push_back(a);
  }
  make_tree(1);
  ans[1] = n;
  solve(1, n + 1, n, 0);
  for (int i = (1); i <= int(n); i++) W(ans[i]);
}
}  // namespace shik
}  // namespace
int main() {
  shik::main();
  return 0;
}
