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>
using std::string;
using std::vector;
namespace Template {
struct IN {
  template <class T>
  void fr(T& a) {
    T s = 0;
    int w = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
      if (ch == '-') w = -1;
      ch = getchar();
    }
    while (ch >= '0' && ch <= '9') s = s * 10 + ch - '0', ch = getchar();
    a = w * s;
  }
  template <class T>
  T fr() {
    T a;
    fr(a);
    return a;
  }
  IN& operator>>(long long& x) { return fr(x), *this; }
  IN& operator>>(signed& x) { return fr(x), *this; }
  IN& operator>>(unsigned& x) { return fr(x), *this; }
  IN& operator>>(char& c) {
    while (isspace(c = getchar()))
      ;
    return *this;
  }
  IN& operator>>(string& str) {
    char ch;
    while (isspace(ch = getchar()))
      ;
    str = ch;
    while (!isspace(ch = getchar())) str += ch;
    return *this;
  }
} cin;
struct OUT {
  char D[1 << 27], *A = D - 1;
  ~OUT() { fwrite(D, 1, A - D + 1, stdout); }
  template <class T>
  void fw(T x) {
    static char C[20];
    static int f;
    x < 0 ? * ++A = '-', x = -x : 0;
    while (C[++f] = 48 + x % 10, x /= 10)
      ;
    while (*++A = C[f], --f)
      ;
  }
  OUT& operator<<(char c) { return *++A = c, *this; }
  OUT& operator<<(string str) {
    int len = str.length();
    for (int i = 0; i < len; i++) *++A = str[i];
    return *this;
  }
  OUT& operator<<(long long x) { return fw(x), *this; }
  OUT& operator<<(signed x) { return fw(x), *this; }
  OUT& operator<<(unsigned x) { return fw(x), *this; }
} cout;
char endl = '\n';
int DEBUG = 0;
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T abs(T a) {
  return a < 0 ? -a : a;
}
template <class T>
T cmin(T a, T b) {
  return a < b ? a : b;
}
template <class T>
T cmax(T a, T b) {
  return a > b ? a : b;
}
template <class T>
void cswp(T& a, T& b) {
  T t = a;
  a = b;
  b = t;
}
}  // namespace Template
using namespace Template;
const int N = 1e5;
int n, blo, tot = 0, fa[N + 10], len[N + 10], arr[N + 10];
vector<int> E[N + 10];
void adde(int u, int v) { E[u].push_back(v); }
void dfs(int u, int f) {
  fa[u] = f, arr[++tot] = u;
  for (int v : E[u])
    if (v != f) dfs(v, u);
}
int calc(int k) {
  int ret = 0;
  for (int i = 1; i <= n; i++) len[i] = 1;
  for (int i = n; i > 1; i--) {
    int u = arr[i], f = fa[u];
    if (len[f] != -1 && len[u] != -1) {
      if (len[f] + len[u] >= k)
        ret++, len[f] = -1;
      else
        len[f] = cmax(len[f], len[u] + 1);
    }
  }
  return ret;
}
int main() {
  cin >> n;
  blo = sqrt(n * log2(n));
  for (int i = 1; i < n; ++i) {
    int u, v;
    cin >> u >> v;
    adde(u, v), adde(v, u);
  }
  dfs(1, 0), cout << n << endl;
  for (int i = 2; i <= blo; i++) cout << calc(i) << endl;
  for (int i = blo + 1; i <= n;) {
    int f = calc(i), l = i, r = n, pos = 0;
    while (l <= r) {
      int mid = (l + r) >> 1;
      if (calc(mid) == f)
        l = mid + 1, pos = mid;
      else
        r = mid - 1;
    }
    for (; i <= pos; i++) cout << f << endl;
  }
  return 0;
}
