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;
int sp[N + 2][20], lev[N + 2];
void add(int n, int p) {
  sp[n][0] = p;
  for (int i = 1; i < 20; i++)
    if (sp[n][i - 1] != -1) sp[n][i] = sp[sp[n][i - 1]][i - 1];
}
int dis(int u, int v) {
  if (lev[u] < lev[v]) swap(u, v);
  int d = 0;
  for (int i = 20 - 1; i >= 0; i--) {
    if (lev[u] - (1 << i) >= lev[v]) u = sp[u][i], d += (1 << i);
  }
  if (u == v) return d;
  for (int i = 20 - 1; i >= 0; i--) {
    if (sp[u][i] == sp[v][i]) continue;
    u = sp[u][i], v = sp[v][i];
    d += 2 * (1 << i);
  }
  return d + 2;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  memset(sp, -1, sizeof(sp));
  int u = 1, v = 1, pr = 0;
  for (int i = 2; i <= n; i++) {
    int x;
    cin >> x;
    add(i, x);
    lev[i] = lev[x] + 1;
    int a = dis(u, i), b = dis(v, i);
    if (max(a, b) <= pr) {
      cout << pr << " ";
      continue;
    }
    if (a > b) {
      cout << a << " ";
      v = i;
    } else {
      cout << b << " ";
      u = i;
    }
    pr = max(a, b);
  }
  cout << endl;
  return 0;
}
