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 LL = long long;
const int N = 200000 + 5;
const int LOG = 18;
int plca[N][LOG], dis[N], n;
int result[N];
int get_lca(int a, int b) {
  if (dis[a] < dis[b]) std::swap(a, b);
  for (int i = 0; i < LOG; ++i)
    if (dis[a] - dis[b] >> i & 1) a = plca[a][i];
  if (a == b) return a;
  for (int i = LOG - 1; i >= 0; --i) {
    if (plca[a][i] != plca[b][i]) {
      a = plca[a][i];
      b = plca[b][i];
    }
  }
  return plca[a][0];
}
int get_dis(int a, int b) { return dis[a] + dis[b] - 2 * dis[get_lca(a, b)]; }
int main() {
  scanf("%d", &n);
  int da = 1, db = 1;
  for (int i = 2; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    plca[i][0] = x;
    dis[i] = dis[x] + 1;
    for (int j = 1; j < LOG; ++j) {
      plca[i][j] = plca[plca[i][j - 1]][j - 1];
    }
    if (get_dis(i, da) > get_dis(da, db))
      db = i;
    else if (get_dis(i, db) > get_dis(da, db))
      da = i;
    result[i] = get_dis(da, db);
  }
  for (int i = 2; i <= n; ++i) {
    printf("%d%c", result[i], " \n"[i == n]);
  }
}
