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 u, v;
int par[19][200055];
int depth[200055];
int get(int u, int v) {
  if (depth[u] > depth[v]) swap(u, v);
  for (int i = 0; i < 18; i++) {
    if (((depth[v] - depth[u]) >> i) & 1) {
      v = par[i][v];
    }
  }
  if (u == v) return u;
  for (int i = 17; i >= 0; i--) {
    if (par[i][u] != par[i][v]) {
      u = par[i][u];
      v = par[i][v];
    }
  }
  return par[0][u];
}
int dist(int u, int v) {
  int lca = get(u, v);
  return (depth[u] - depth[lca]) + (depth[v] - depth[lca]);
}
int main() {
  scanf("%d", &n);
  u = 0, v = 0;
  int res = 0;
  int x;
  memset(par, -1, sizeof(par));
  for (int i = 1; i < n; i++) {
    scanf("%d", &x);
    x--;
    par[0][i] = x;
    depth[i] = depth[x] + 1;
    for (int j = 0; j < 17; j++) {
      if (par[j][i] == -1)
        par[j + 1][i] = -1;
      else
        par[j + 1][i] = par[j][par[j][i]];
    }
    int a = dist(i, u);
    int b = dist(i, v);
    if (max(a, b) > res) {
      res = max(a, b);
      if (max(a, b) == a)
        v = i;
      else
        u = i;
    }
    printf("%d\n", res);
  }
  return 0;
}
