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 P = 1000000007;
const int N = 300200;
vector<int> e[N];
int deep[N], jump[N][20];
int n, m, a, b, i, cnt;
int l, r;
void dfs(int x, int fa) {
  int i;
  deep[x] = deep[fa] + 1;
  jump[x][0] = fa;
  for (i = 1; i <= 18; i++) jump[x][i] = jump[jump[x][i - 1]][i - 1];
  for (i = 0; i < e[x].size(); i++)
    if (e[x][i] != fa) dfs(e[x][i], x);
}
int lca(int a, int b) {
  if (deep[a] < deep[b]) a ^= b ^= a ^= b;
  int i;
  for (i = 18; i >= 0; i--)
    if (deep[jump[a][i]] >= deep[b]) a = jump[a][i];
  if (a == b) return a;
  for (i = 18; i >= 0; i--)
    if (jump[a][i] != jump[b][i]) a = jump[a][i], b = jump[b][i];
  return jump[a][0];
}
int dis(int a, int b) { return deep[a] + deep[b] - 2 * deep[lca(a, b)]; }
int main() {
  scanf("%d", &n);
  for (i = 2; i <= n; i++) {
    scanf("%d", &a);
    e[a].push_back(i);
  }
  dfs(1, 0);
  a = 1;
  b = 1;
  int tmp = 0;
  for (i = 2; i <= n; i++) {
    int t1 = dis(a, i);
    int t2 = dis(b, i);
    printf("%d ", max(tmp, max(t1, t2)));
    if (max(t1, t2) > tmp) {
      tmp = max(t1, t2);
      if (t1 > t2)
        b = i;
      else
        a = i;
    }
  }
}
