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 long N = 200002, MAXLOG = 19;
long h[N];
long dp[N][MAXLOG];
void add(long cur, long parent) {
  h[cur] = h[parent] + 1;
  dp[cur][0] = parent;
  for (int i = 1; i < MAXLOG; i++) {
    dp[cur][i] = dp[dp[cur][i - 1]][i - 1];
  }
}
long get_LCA(long u, long v) {
  if (h[v] > h[u]) {
    swap(u, v);
  }
  int k = ceil(log2(h[u]));
  for (int i = k; i >= 0; i--) {
    if (h[dp[u][i]] >= h[v]) {
      u = dp[u][i];
    }
  }
  if (v == u) {
    return v;
  }
  for (int i = k; i >= 0; i--) {
    if (dp[u][i] != dp[v][i]) {
      u = dp[u][i];
      v = dp[v][i];
    }
  }
  return dp[v][0];
}
int main() {
  ios::sync_with_stdio(false);
  long n;
  cin >> n;
  long dist = 0;
  long node1 = 1, node2 = 1;
  h[1] = 1;
  for (long i = 2; i <= n; i++) {
    long in;
    cin >> in;
    add(i, in);
    long LCA = get_LCA(i, node1), temp = -1;
    if (dist < abs(h[i] - h[LCA]) + abs(h[node1] - h[LCA])) {
      dist = abs(h[i] - h[LCA]) + abs(h[node1] - h[LCA]);
      temp = i;
    }
    LCA = get_LCA(i, node2);
    if (dist < abs(h[i] - h[LCA]) + abs(h[node2] - h[LCA])) {
      dist = abs(h[i] - h[LCA]) + abs(h[node2] - h[LCA]);
      node1 = i;
      temp = -1;
    }
    if (temp > -1) {
      node2 = temp;
    }
    cout << dist << ' ';
  }
  return 0;
}
