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 logN = 18;
vector<int> depth;
vector<vector<int> > ancestor;
void add(int u, int v) {
  depth[u] = depth[v] + 1;
  ancestor[u][0] = v;
  for (int i = 1; i < logN; ++i) {
    ancestor[u][i] = ancestor[ancestor[u][i - 1]][i - 1];
  }
}
int LCA(int u, int v) {
  if (depth[u] < depth[v]) swap(u, v);
  for (int i = logN - 1; i >= 0; --i) {
    if (depth[u] - depth[v] >= (1 << i)) u = ancestor[u][i];
  }
  if (u == v) return u;
  for (int i = logN - 1; i >= 0; --i) {
    if (ancestor[u][i] != ancestor[v][i]) {
      u = ancestor[u][i];
      v = ancestor[v][i];
    }
  }
  return ancestor[u][0];
}
int distance(int u, int v) {
  int temp = LCA(u, v);
  return depth[u] + depth[v] - 2 * depth[temp];
}
int main() {
  std::ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  depth = vector<int>(n + 1);
  ancestor = vector<vector<int> >(n + 1, vector<int>(logN));
  for (int i = 0; i != logN; ++i) {
    ancestor[1][i] = 1;
  }
  int node1 = 1, node2 = 1, currentLatency = 0;
  for (int i = 2; i != n + 1; ++i) {
    int node;
    cin >> node;
    add(i, node);
    int temp1 = distance(i, node1);
    int temp2 = distance(i, node2);
    if (temp1 >= temp2 && temp1 > currentLatency) {
      currentLatency = temp1;
      node2 = i;
    } else if (temp2 > temp1 && temp2 > currentLatency) {
      currentLatency = temp2;
      node1 = i;
    }
    cout << currentLatency << " ";
  }
  cout << endl;
}
