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;
int d[212345];
int dx = 1;
int p[18][212345];
int lca(int a, int b) {
  if (d[a] < d[b]) swap(a, b);
  int dff = d[a] - d[b];
  for (int i = 0; i < 18; i++) {
    if ((dff >> i) & 1) a = p[i][a];
  }
  if (a == b) return a;
  for (int i = 17; i >= 0; i--) {
    if (p[i][a] != p[i][b]) {
      a = p[i][a];
      b = p[i][b];
    }
  }
  return p[0][a];
  return a;
}
int len(int a, int b) { return d[a] + d[b] - 2 * d[lca(a, b)]; }
int main() {
  int n;
  cin >> n;
  int a, b;
  d[1] = 1;
  p[0][1] = 1;
  int cr = 1;
  int cl = 2;
  for (int i = 2; i < n + 1; i++) {
    int u;
    cin >> u;
    d[i] = d[u] + 1;
    p[0][i] = u;
    for (int j = 1; j < 18; j++) {
      p[j][i] = p[j - 1][p[j - 1][i]];
    }
    if (i > 2) {
      if (dx < len(cr, i)) {
        dx = len(cr, i);
        cl = i;
      }
      if (dx < len(cl, i)) {
        cr = i;
        dx = len(cl, i);
      }
    }
    cout << dx << " ";
  }
}
