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 = 2e5 + 1;
int n, m;
int dp[N][18], lvl[N];
int lca(int a, int b) {
  if (lvl[a] < lvl[b]) swap(a, b);
  for (int i = 17; i >= 0; i--)
    if (lvl[dp[a][i]] >= lvl[b]) a = dp[a][i];
  if (a == b) return a;
  for (int i = 17; i >= 0; i--)
    if (dp[a][i] != dp[b][i]) a = dp[a][i], b = dp[b][i];
  if (a == b) return a;
  return dp[a][0];
}
int dist(int a, int b) { return lvl[a] + lvl[b] - 2 * lvl[lca(a, b)]; }
int main() {
  scanf("%d", &n);
  int p;
  int a = 0, b = 0;
  int best = 0;
  for (int i = 1; i < n; i++) {
    scanf("%d", &p);
    --p;
    lvl[i] = lvl[p] + 1;
    dp[i][0] = p;
    for (int j = 1; (1 << j) <= lvl[i]; j++) dp[i][j] = dp[dp[i][j - 1]][j - 1];
    if (a == p)
      a = i, ++best;
    else if (b == p)
      b = i, ++best;
    else {
      int da = dist(a, i), db = dist(b, i);
      if (da > best) best = da, b = i;
      if (db > best) best = db, a = i;
    }
    printf("%d ", best);
  }
  putchar('\n');
  return 0;
}
