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 MOD = 1000000007;
double PI = 4 * atan(1);
int depth[200001], par[200001][18], a = 1, b = 1, c = 0;
int lca(int v1, int v2) {
  if (depth[v1] > depth[v2]) swap(v1, v2);
  int z = depth[v2] - depth[v1];
  for (int i = 0; i < 18; i++)
    if (z & (1 << i)) v2 = par[v2][i];
  if (v1 == v2) return v1;
  for (int i = 17; i >= 0; --i) {
    if (par[v1][i] != par[v2][i]) v1 = par[v1][i], v2 = par[v2][i];
  }
  return par[v1][0];
}
int dist(int v1, int v2) {
  int ans = 0;
  int z = lca(v1, v2);
  return (depth[v1] + depth[v2] - 2 * depth[z]);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 2; i < n + 1; i++) {
    cin >> par[i][0];
    depth[i] = depth[par[i][0]] + 1;
    for (int j = 1; j < 18; j++) par[i][j] = par[par[i][j - 1]][j - 1];
    int c1 = dist(a, i), c2 = dist(b, i);
    if (c1 > c && c1 >= c2)
      c++, b = i;
    else if (c2 > c && c2 > c1)
      c++, a = i;
    cout << c << " ";
  }
}
