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, f;
int d[200007];
int p[18][200007];
bool child(int a, int b) {
  for (int i = 18 - 1; i >= 0; --i) {
    if (p[i][a] >= b) a = p[i][a];
  }
  return a == b;
}
int lca(int a, int b) {
  if (child(a, b)) return b;
  if (child(b, a)) return a;
  int l = 18 - 1;
  while (l >= 0) {
    if (child(b, p[l][a]))
      --l;
    else
      a = p[l][a];
  }
  return p[0][a];
}
int dist(int a, int b) { return d[a] + d[b] - 2 * d[lca(a, b)]; }
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cin >> n;
  for (int i = 0; i < 18; ++i) {
    p[i][1] = 1;
  }
  int a = 1, b = 1, curr = 0;
  for (int i = 2; i <= n; ++i) {
    cin >> f;
    d[i] = d[f] + 1;
    p[0][i] = f;
    for (int j = 1; j < 18; ++j) {
      p[j][i] = p[j - 1][p[j - 1][i]];
    }
    int d1 = dist(a, i);
    if (d1 > curr) {
      curr = d1;
      b = i;
    }
    int d2 = dist(i, b);
    if (d2 > curr) {
      curr = d2;
      a = i;
    }
    cout << curr << " ";
  }
}
