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 p[22][200010], dp[200010], n;
int LCA(int i, int j) {
  int k;
  if (dp[i] < dp[j]) i ^= j ^= i ^= j;
  for (k = 0; (1 << k) <= dp[i]; k++)
    ;
  k--;
  for (int u = k; u >= 0; u--)
    if (dp[i] - (1 << u) >= dp[j]) i = p[u][i];
  if (i != j) {
    for (int u = k; u >= 0; u--)
      if (p[u][i] != p[u][j]) i = p[u][i], j = p[u][j];
    i = p[0][i];
  }
  return i;
}
int main() {
  scanf("%d", &n);
  int d = 1, a = 1, b = 2, x;
  scanf("%d", &x);
  p[0][2] = 1;
  dp[1] = 1;
  dp[2] = 2;
  printf("%d ", 1);
  for (int i = 3; i <= n; i++) {
    scanf("%d", &x);
    p[0][i] = x;
    dp[i] = dp[x] + 1;
    for (int j = 1; j <= 20; j++) p[j][i] = p[j - 1][p[j - 1][i]];
    int z = LCA(a, i);
    int A = dp[a] + dp[i] - 2 * dp[z];
    z = LCA(b, i);
    int B = dp[b] + dp[i] - 2 * dp[z];
    int bf = 0;
    if (A > B) bf = 1;
    if (max(A, B) > d) {
      d = max(A, B);
      if (bf)
        b = i;
      else
        a = i;
    }
    printf("%d ", d);
  }
}
