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 = 200200;
int d[N], dp[N][20], n;
int lca(int a, int b) {
  if (d[a] < d[b]) swap(a, b);
  int k = d[a] - d[b];
  for (int i = 0; i < 20; i++) {
    if ((k >> i) & 1) {
      a = dp[a][i];
    }
  }
  if (a != b) {
    for (int i = 19; i >= 0; i--) {
      if (dp[a][i] != dp[b][i]) {
        a = dp[a][i];
        b = dp[b][i];
      }
    }
    a = dp[a][0];
  }
  return a;
}
int dist(int a, int b) {
  int u = lca(a, b);
  return d[a] + d[b] - 2 * d[u];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  d[1] = 0;
  int max_diam = 1;
  int n1 = 1, n2 = 2;
  for (int i = 2; i <= n; i++) {
    cin >> dp[i][0];
    d[i] = d[dp[i][0]] + 1;
    for (int j = 0; j < 20; j++) {
      if (dp[i][j] != 0) {
        dp[i][j + 1] = dp[dp[i][j]][j];
      }
    }
    if (i == 2) {
      cout << 1 << '\n';
      continue;
    }
    int d1 = dist(i, n1);
    int d2 = dist(i, n2);
    int dd, tn1, tn2;
    if (d1 > d2) {
      dd = d1;
      tn1 = n1;
      tn2 = i;
    } else {
      dd = d2;
      tn1 = i;
      tn2 = n2;
    }
    if (dd > max_diam) {
      max_diam = dd;
      n1 = tn1;
      n2 = tn2;
    }
    cout << max_diam << '\n';
  }
  return 0;
}
