#include <bits/stdc++.h>
using namespace std;
int n;
vector<int> G[200001];
int root = 0;
int parent[21][200001];
int depth[200001];
void dfs(int v, int p, int d) {
  parent[0][v] = p;
  depth[v] = d;
  for (int i = 0; i < G[v].size(); i++) {
    if (G[v][i] != p) {
      dfs(G[v][i], v, d + 1);
    }
  }
}
void init() {
  dfs(root, -1, 0);
  for (int k = 0; k + 1 < 20; k++) {
    for (int v = 0; v < n; v++) {
      if (parent[k][v] < 0) {
        parent[k + 1][v] = -1;
      } else {
        parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }
}
int lca(int u, int v) {
  if (depth[u] > depth[v]) {
    swap(u, v);
  }
  int res = 0;
  for (int k = 0; k < 20; k++) {
    if (((depth[v] - depth[u]) >> k) & 1) {
      res += 1 << k;
      v = parent[k][v];
    }
  }
  if (u == v) return res;
  for (int k = 19; k >= 0; k--) {
    if (parent[k][u] != parent[k][v]) {
      res += (1 << (k + 1));
      u = parent[k][u];
      v = parent[k][v];
    }
  }
  return res + 2;
}
int res[200001];
int main(void) {
  scanf("%d", &n);
  for (int i = 1; i <= n - 1; i++) {
    int a;
    scanf("%d", &a);
    a--;
    G[i].push_back(a);
    G[a].push_back(i);
  }
  init();
  int df = 0, dt = 1;
  res[0] = 1;
  for (int i = 2; i < n; i++) {
    if (lca(df, dt) < lca(i, df)) {
      dt = i;
    }
    if (lca(df, dt) < lca(i, dt)) {
      df = i;
    }
    res[i - 1] = lca(df, dt);
  }
  for (int i = 0; i < n - 1; i++) {
    printf("%d%c", res[i], i + 1 == n - 1 ? '\n' : ' ');
  }
  return 0;
}
