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;
const int LN = 18;
int n;
int dp[LN][N];
int depth[N];
int a, b;
int dia;
int lca(int a, int b) {
  if (depth[a] < depth[b]) {
    swap(a, b);
  }
  int dif = depth[a] - depth[b];
  for (int i = 0; i < LN; ++i) {
    if (dif & (1 << i)) {
      a = dp[i][a];
    }
  }
  if (a != b) {
    for (int i = LN - 1; i >= 0; --i) {
      if (dp[i][a] != dp[i][b]) {
        a = dp[i][a];
        b = dp[i][b];
      }
    }
    a = dp[0][a];
  }
  return a;
}
int dist(int a, int b) { return depth[a] + depth[b] - (depth[lca(a, b)] << 1); }
int main() {
  scanf("%d", &n);
  dp[0][1] = 0;
  depth[1] = 0;
  a = 1;
  b = 1;
  dia = 0;
  for (int i = 2; i <= n; ++i) {
    scanf("%d", &dp[0][i]);
    depth[i] = depth[dp[0][i]] + 1;
    for (int j = 1; j < LN; ++j) {
      dp[j][i] = dp[j - 1][dp[j - 1][i]];
    }
    int val1 = dist(i, a);
    int val2 = dist(i, b);
    if (val1 < val2) {
      swap(val1, val2);
      swap(a, b);
    }
    if (val1 > dia) {
      b = i;
      dia = val1;
    }
    printf("%d%c", dia, " \n"[i == n]);
  }
}
