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 + 5;
int p[N][22], d[N], D = 1, add;
int lca(int a, int b) {
  if (d[a] < d[b]) swap(a, b);
  int i, diff = d[a] - d[b];
  for (i = 0; i < 22; ++i)
    if (diff & (1 << i)) a = p[a][i];
  if (a == b) return a;
  for (i = 21; i >= 0; --i)
    if (p[a][i] != p[b][i]) a = p[a][i], b = p[b][i];
  a = p[a][0];
  return a;
}
int s, t;
void go(int a, int b, int c) {
  int tem = d[a] + d[c] - 2 * d[lca(a, c)];
  if (tem > D) s = a, t = c, D = tem;
  tem = d[b] + d[c] - 2 * d[lca(b, c)];
  if (tem > D) s = b, t = c, D = tem;
}
int main() {
  int j, n, i, u;
  s = 1, t = 2;
  cin >> n;
  for (i = 2; i <= n; ++i) {
    scanf("%d", &u);
    d[i] = d[u] + 1;
    p[i][0] = u;
    for (j = 1; j < 22; ++j) p[i][j] = p[p[i][j - 1]][j - 1];
    go(s, t, i);
    printf("%d\n", D);
  }
}
