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 target("avx,avx2")
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
template <typename T1, typename T2>
inline void chkmin(T1 &x, const T2 &y) {
  if (x > y) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1 &x, const T2 &y) {
  if (x < y) x = y;
}
int ptr = 0;
char memory[(int)20 * 1024 * 1024];
inline void *operator new(size_t n) {
  char *res = memory + ptr;
  ptr += n;
  return (void *)res;
}
inline void operator delete(void *) noexcept {}
inline void operator delete(void *, size_t) {}
namespace fast {
template <class T = int>
inline T readInt();
inline double readDouble();
inline int readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int getChar();
inline int peekChar();
inline bool seekEof();
inline void skipBlanks();
template <class T>
inline void writeInt(T x, char end = 0, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(double x, int len = 0);
inline void flush();
static struct buffer_flusher_t {
  ~buffer_flusher_t() { flush(); }
} buffer_flusher;
static const int buf_size = 4096;
static unsigned char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline void skipBlanks() {
  while (!isEof() && buf[buf_pos] <= 32U) buf_pos++;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline int readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-')
    s = -1, c = getChar();
  else if (c == '+')
    c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline double readDouble() {
  int s = 1, c = readChar();
  double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 1e-1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = x;
}
inline void flush() {
  if (write_buf_pos) {
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
    fflush(stdout);
  }
}
template <class T>
inline void writeInt(T x, char end, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
  if (end) writeChar(end);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
}  // namespace fast
using namespace fast;
const int MAXN = 1e5 + 230;
int n;
vector<int> g[MAXN];
int deg[MAXN];
int p[MAXN];
int tin[MAXN], timer = 0;
int len[MAXN];
int cost[MAXN];
int res;
int ans[MAXN];
void read() {
  n = readInt();
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    u = readInt();
    v = readInt();
    u--;
    v--;
    deg[u]++;
    deg[v]++;
    g[u].push_back(v);
    g[v].push_back(u);
  }
}
void dfs_tin(int v, int pv, int last_good) {
  if (v == 0 || deg[v] != 2) {
    tin[v] = timer++;
    len[v] = 0;
    cost[tin[v]] = len[pv] + 1;
    p[tin[v]] = last_good;
    last_good = tin[v];
  } else {
    len[v] = len[pv] + 1;
  }
  for (auto i : g[v]) {
    if (i == pv) continue;
    dfs_tin(i, v, last_good);
  }
}
void build() {
  dfs_tin(0, 0, 0);
  reverse(p, p + timer);
  reverse(cost, cost + timer);
  for (int i = 0; i < timer; ++i) {
    p[i] = timer - 1 - p[i];
    tin[i] = 0;
    len[i] = 0;
  }
}
void dfs(int k) {
  if (k == 1) {
    res = n;
    return;
  }
  res = 0;
  for (int v = 0; v < timer; ++v) {
    if (len[v]) {
      res++;
      tin[v] = -1;
    }
    tin[v] += cost[v];
    while (tin[v] >= k) res++, tin[v] -= k;
    if (tin[v] + tin[p[v]] + 1 >= k) {
      len[p[v]] = 1;
    }
    if (tin[v] > tin[p[v]]) {
      tin[p[v]] = tin[v];
    }
    len[v] = tin[v] = 0;
  }
}
int calc(int k) {
  dfs(k);
  return res;
}
void solve(int lk, int rk, int min_val, int max_val) {
  chkmin(max_val, n / lk);
  if (min_val == max_val) {
    for (int i = lk; i <= rk; ++i) {
      ans[i] = min_val;
    }
    return;
  }
  int mk = (lk + rk) >> 1;
  ans[mk] = calc(mk);
  if (lk <= mk - 1) {
    solve(lk, mk - 1, ans[mk], max_val);
  }
  if (mk + 1 <= rk) {
    solve(mk + 1, rk, min_val, ans[mk]);
  }
}
void run() {
  build();
  solve(1, n, 0, n);
}
void write() {
  for (int i = 1; i <= n; ++i) {
    writeInt(ans[i], '\n');
  }
}
signed main() {
  read();
  run();
  write();
  return 0;
}
