#ifdef LOCAL
#include "stdafx.h"
#else
#include <bits/stdc++.h>
#define IL inline
#define LL long long
#define eb emplace_back
#define sz(v) ((int) (v).size())
#define L(i, j, k) for (int i = (j); i <= (k); ++i)
#define R(i, j, k) for (int i = (j); i >= (k); --i)
#define FIO(FILE) freopen(FILE".in", "r", stdin), freopen(FILE".out", "w", stdout)
using namespace std;

using vi = vector<int>;
#endif

constexpr int N = 2e5 + 9;
int n, deg[N], sz[N], ns[N];
vi g[N], e[N / 2];

bool vis[N];

int dfn[N], dfc, st[18][N], d[N];

void dfs (int u, int f) {
  d[u] = d[f] + 1;
  st[0][dfn[u] = ++dfc] = f;
  for (int v : g[u]) {
    if (v ^ f) {
      dfs(v, u);
    }
  }
}

IL int cp (int x, int y) {
  return dfn[x] < dfn[y] ? x : y;
}

IL int lca (int x, int y) {
  if (x == y) {
    return x;
  }
  if ((x = dfn[x]) > (y = dfn[y])) {
    swap(x, y);
  }
  int i = __lg(y - x++);
  return cp(st[i][x], st[i][y - (1 << i) + 1]);
}

IL int dis (int x, int y) {
  return d[x] + d[y] - 2 * d[lca(x, y)];
}

int main () {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n;
  L (i, 1, n - 1) {
    int u, v;
    cin >> u >> v;
    g[u].eb(v);
    g[v].eb(u);
  }
  dfs(1, 0);
  L (i, 1, 17) {
    L (j, 1, n - (1 << i) + 1) {
      st[i][j] = cp(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
    }
  }
  L (i, 1, n) {
    deg[i] = sz(g[i]);
  }
  priority_queue<pair<int, int>> q;
  L (i, 1, n) {
    sz[i] = 1;
    if (deg[i] == 1) {
      q.emplace(-sz[i], i);
    }
  }
  while (-q.top().first <= n / 2) {
    int u = q.top().second;
    q.pop();
    vis[u] = true;
    for (int v : g[u]) {
      if (!vis[v]) {
        e[sz[u] + 1].eb(u);
        sz[v] += sz[u];
      }
      if ((--deg[v]) == 1) {
        q.emplace(-sz[v], v);
      }
    }
  }
  int L, R;
  L = R = q.top().second;
  R (i, n / 2 + 1, 1) {
    ns[i] = dis(L, R);
    for (auto u : e[i]) {
      cout << i << ' ' << u << '\n';
      if (dis(L, u) > dis(L, R)) {
        R = u;
      }
      if (dis(u, R) > dis(L, R)) {
        L = u;
      }
    }
  }
  L (i, 1, n) {
    cout << (i & 1 ? 1 : ns[i / 2] + 1) << '\n';
  }
}
// I love WHQ!