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 n;
int fa[200003];
int nowl, nowr, nowans;
int f[200003][23];
int dep[200003];
inline int lca(int a, int b) {
  if (dep[a] < dep[b]) {
    swap(a, b);
  }
  int x = dep[a] - dep[b];
  for (int i = 0; i <= 20; i++) {
    if (x & (1 << i)) {
      a = f[a][i];
    }
  }
  for (int i = 20; i >= 0; i--) {
    if (f[a][i] != f[b][i]) {
      a = f[a][i], b = f[b][i];
    }
  }
  if (a == b) {
    return a;
  }
  return f[a][0];
}
inline int ju(int a, int b) {
  if (a == b) {
    return 0;
  }
  int ca = lca(a, b);
  return dep[a] + dep[b] - 2 * dep[ca];
}
int main() {
  cin >> n;
  nowl = 1, nowr = 1;
  nowans = 0;
  f[1][0] = 0;
  dep[1] = 1;
  for (int i = 2; i <= n; i++) {
    cin >> fa[i];
    dep[i] = dep[fa[i]] + 1;
    f[i][0] = fa[i];
    for (int j = 1; j <= 20; j++) {
      f[i][j] = f[f[i][j - 1]][j - 1];
    }
    if (ju(nowl, i) >= nowans && ju(nowl, i) >= ju(nowr, i)) {
      nowans = ju(nowl, i);
      nowr = i;
    }
    if (ju(nowr, i) >= nowans && ju(nowr, i) >= ju(nowl, i)) {
      nowans = ju(nowr, i);
      nowl = i;
    }
    cout << nowans << endl;
  }
  return 0;
}
