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 depth[200005];
int up[200005][25];
int father[200005];
int lca(int x, int y) {
  if (depth[x] < depth[y]) swap(x, y);
  int t = depth[x] - depth[y];
  int i;
  for (i = 0; i < 20; i++) {
    if ((1 << i) & t) x = up[x][i];
  }
  for (i = 19; i >= 0; i--) {
    if (up[x][i] == up[y][i]) continue;
    x = up[x][i];
    y = up[y][i];
  }
  return father[x];
}
int main() {
  int n;
  scanf("%d", &n);
  int i;
  int farest_point = 0;
  int farest_depth = 0;
  int ans = 0;
  for (i = 0; i < 20; i++) {
    up[0][i] = -1;
  }
  for (i = 1; i < n; i++) {
    int x;
    scanf("%d", &x);
    x--;
    father[i] = x;
    depth[i] = depth[x] + 1;
    int j;
    up[i][0] = x;
    for (j = 1; j < 20; j++) {
      if (up[i][j - 1] == -1) {
        up[i][j] = -1;
      } else {
        up[i][j] = up[up[i][j - 1]][j - 1];
      }
    }
    if (depth[i] > farest_depth) {
      farest_point = i;
      ans++;
      farest_depth++;
      printf("%d ", ans);
      continue;
    }
    int t = lca(i, farest_point);
    if (depth[i] - depth[t] + farest_depth - depth[t] > ans) {
      ans++;
    }
    printf("%d ", ans);
  }
  return 0;
}
