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 M = 200005;
int dp[M][20];
void calc(int u) {
  for (int i = 1; i <= 18; i++) {
    int v = dp[u][i - 1];
    if (v != -1) dp[u][i] = dp[v][i - 1];
  }
}
int dist_root(int u) {
  int ans = 0;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] == -1) continue;
    u = dp[u][i], ans += (1 << i);
  }
  return ans;
}
int lca(int u, int v) {
  int a = dist_root(u), b = dist_root(v);
  if (a < b) swap(u, v);
  int ans = abs(a - b), alt = ans;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] == -1) continue;
    if (alt - (1 << i) >= 0) {
      alt -= (1 << i);
      u = dp[u][i];
    }
  }
  if (u == v) return ans;
  for (int i = 18; i >= 0; i--) {
    if (dp[u][i] != -1 && dp[u][i] != dp[v][i]) {
      ans += (1 << (i + 1));
      u = dp[u][i];
      v = dp[v][i];
    }
  }
  return ans + 2;
}
int main() {
  memset(dp, -1, sizeof dp);
  int n, u = 1, v = 1, ma = -1;
  scanf("%d", &n);
  vector<int> ans;
  for (int i = 2; i <= n; i++) {
    int a;
    scanf("%d", &a);
    dp[i][0] = a;
    calc(i);
    int x = lca(u, i);
    int y = lca(v, i);
    if (ma >= max(x, y)) {
      ans.push_back(ma);
      continue;
    }
    if (x > y) {
      v = i;
      ma = x;
    } else {
      u = i;
      ma = y;
    }
    ans.push_back(ma);
  }
  for (int i = 0; i < ans.size(); i++) printf("%d ", ans[i]);
  return 0;
}
