#include <bits/stdc++.h>
using namespace std;
const int M = 200005;
int dp[M][20];
void calc(int u) {
  for (int i = 1; i <= 18; i++) {
    int v = dp[u][i - 1];
    if (v != -1) dp[u][i] = dp[v][i - 1];
  }
}
int dist_root(int u) {
  int ans = 0;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] == -1) continue;
    u = dp[u][i], ans += (1 << i);
  }
  return ans;
}
int lca(int u, int v) {
  int a = dist_root(u), b = dist_root(v);
  if (a < b) swap(u, v);
  int ans = abs(a - b), alt = ans;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] == -1) continue;
    if (alt - (1 << i) >= 0) {
      alt -= (1 << i);
      u = dp[u][i];
    }
  }
  if (u == v) return ans;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] != -1 && dp[u][i] != dp[v][i]) {
      ans += (1 << (i + 1));
      u = dp[u][i];
      v = dp[v][i];
    }
  }
  return ans + 2;
}
int main() {
  memset(dp, -1, sizeof dp);
  int n, u = 1, v = 1, ma = -1;
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) {
    int a;
    scanf("%d", &a);
    dp[i][0] = a;
    calc(i);
    int x = lca(u, i);
    int y = lca(v, i);
    if (ma >= max(x, y)) {
      printf("%d ", ma);
      continue;
    }
    if (x > y) {
      v = i;
      ma = x;
    } else {
      u = i;
      ma = y;
    }
    printf("%d ", ma);
  }
  return 0;
}
