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 P[200050][20], level[200050];
int n, a = 1, b = 2;
vector<int> edge[200050];
void init(int at, int par) {
  level[at] = level[par] + 1;
  P[at][0] = par;
  for (int i = 1; i < 19; i++) {
    P[at][i] = P[P[at][i - 1]][i - 1];
  }
}
int lca(int x, int y) {
  if (level[x] < level[y]) swap(x, y);
  for (int i = 19; i >= 0; i--) {
    if (level[x] - (1 << i) >= level[y]) {
      x = P[x][i];
    }
  }
  if (x == y) return x;
  for (int i = 19; i >= 0; i--) {
    if (P[x][i] != P[y][i]) {
      x = P[x][i];
      y = P[y][i];
    }
  }
  return P[x][0];
}
int dist(int x, int y) { return level[x] + level[y] - level[lca(x, y)] * 2; }
int solve(int at) {
  int r1 = dist(a, b);
  int r2 = dist(a, at);
  int r3 = dist(b, at);
  int ret = max(r1, max(r2, r3));
  if (r2 == ret) {
    a = a;
    b = at;
  } else if (r3 == ret) {
    a = b;
    b = at;
  }
  return ret;
}
int main() {
  int x, y;
  scanf("%d", &n);
  scanf("%d", &x);
  init(2, x);
  printf("1");
  for (int i = 3; i <= n; i++) {
    scanf("%d", &x);
    init(i, x);
    printf(" %d", solve(i));
  }
  printf("\n");
  return 0;
}
