Breaking news from zombie neurology! It turns out that – contrary to previous beliefs – every zombie is born with a single brain, and only later it evolves into a complicated brain structure. In fact, whenever a zombie consumes a brain, a new brain appears in its nervous system and gets immediately connected to one of the already existing brains using a single brain connector. Researchers are now interested in monitoring the brain latency of a zombie. Your task is to write a program which, given a history of evolution of a zombie's nervous system, computes its brain latency at every stage.

Input

The first line of the input contains one number n – the number of brains in the final nervous system (2 ≤ n ≤ 200000). In the second line a history of zombie's nervous system evolution is given. For convenience, we number all the brains by 1, 2, ..., n in the same order as they appear in the nervous system (the zombie is born with a single brain, number 1, and subsequently brains 2, 3, ..., n are added). The second line contains n - 1 space-separated numbers p2, p3, ..., pn, meaning that after a new brain k is added to the system, it gets connected to a parent-brain <image>.

Output

Output n - 1 space-separated numbers – the brain latencies after the brain number k is added, for k = 2, 3, ..., n.

Example

Input

6
1
2
2
1
5


Output

1 2 2 3 4 
#include <bits/stdc++.h>
using namespace std;
const int DEBUG = 1;
const int MAX = 2e5 + 10;
const int LOG = 20;
int par[MAX][LOG], n, h[MAX];
void update_par(int node, int p) {
  par[node][0] = p;
  if (p + 1) h[node] = h[p] + 1;
  for (int(k) = (1); (k) < (LOG); (k)++) {
    if (par[node][k - 1] + 1) {
      par[node][k] = par[par[node][k - 1]][k - 1];
    }
  }
}
int LCA(int a, int b) {
  if (h[a] < h[b]) swap(a, b);
  for (int k = LOG - 1; k >= 0; k--) {
    if (par[a][k] + 1 && h[par[a][k]] >= h[b]) a = par[a][k];
  }
  if (a == b) return a;
  for (int k = LOG - 1; k >= 0; k--)
    if (par[a][k] != par[b][k]) {
      a = par[a][k];
      b = par[b][k];
    }
  return par[a][0];
}
int get_dist(int a, int b) {
  int lowest = LCA(a, b);
  return h[a] + h[b] - 2 * h[lowest];
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  memset(par, -1, sizeof(par));
  int u = 1, v = 1;
  int p;
  for (int(cur) = (2); (cur) < (n + 1); (cur)++) {
    cin >> p;
    update_par(cur, p);
    int one = get_dist(u, v);
    int two = get_dist(cur, u);
    int three = get_dist(cur, v);
    int maxi = max(one, max(two, three));
    cout << maxi << ' ';
    if (two == maxi) {
      v = cur;
    } else if (three == maxi) {
      u = cur;
    }
  }
  cout << "\n";
}
