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 inf = 987654321;
const long long int INF = 123456789987654321;
vector<int> dep;
vector<vector<int> > par;
int lca(int a, int b) {
  if (dep[a] < dep[b]) swap(a, b);
  int diff = dep[a] - dep[b];
  for (int i = 0; i < 19; i++) {
    if ((diff >> i) & 1) a = par[i][a];
  }
  if (a == b) return a;
  for (int i = 19; i--;) {
    if (par[i][a] != par[i][b]) {
      a = par[i][a];
      b = par[i][b];
    }
  }
  return par[0][a];
}
int dist(int a, int b) {
  int x = lca(a, b);
  return dep[a] + dep[b] - 2 * dep[x];
}
int N;
int main() {
  scanf("%d", &N);
  dep = vector<int>(N, 0);
  par = vector<vector<int> >(19, vector<int>(N, -1));
  int now = 1;
  pair<int, int> cur = pair<int, int>(0, 0);
  for (int i = 0; i < N - 1; i++) {
    int p;
    scanf("%d", &p);
    p--;
    dep[now] = dep[p] + 1;
    par[0][now] = p;
    for (int i = 1; i < 19; i++) {
      int t = par[i - 1][now];
      if (t == -1) break;
      par[i][now] = par[i - 1][t];
    }
    int u = cur.first, v = cur.second;
    int D = dist(u, v);
    if (D < dist(u, now)) {
      D = dist(u, now);
      cur = pair<int, int>(u, now);
    }
    if (D < dist(v, now)) {
      D = dist(v, now);
      cur = pair<int, int>(v, now);
    }
    printf("%d ", D);
    now++;
  }
}
