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 N = 2e5 + 5;
int p[18][N], n;
int l[N];
int curl = 1, curr = 2, d = 1;
void upd(int u) {
  for (int i = 1; i <= 17; i++) p[i][u] = p[i - 1][p[i - 1][u]];
}
int lca(int u, int v) {
  if (l[u] < l[v]) swap(u, v);
  for (int i = 17; i >= 0; i--) {
    if (l[p[i][u]] >= l[v]) u = p[i][u];
  }
  for (int i = 17; i >= 0; i--) {
    if (p[i][u] != p[i][v]) {
      u = p[i][u];
      v = p[i][v];
    }
  }
  while (u != v) {
    u = p[0][u];
    v = p[0][v];
  }
  return u;
}
int len(int u, int v) {
  int p = lca(u, v);
  return l[u] + l[v] - 2 * l[p];
}
int main() {
  cin >> n;
  l[1] = 1;
  p[0][1] = 1;
  for (int i = 2; i <= n; i++) {
    int u;
    cin >> u;
    l[i] = l[u] + 1;
    p[0][i] = u;
    upd(i);
    if (i > 2) {
      if (d < len(curl, i)) {
        d = len(curl, i);
        curr = i;
      }
      if (d < len(curr, i)) {
        d = len(curr, i);
        curl = i;
      }
    }
    cout << d << " ";
  }
}
