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 long long maxn = 2e5 + 100;
const long long level = 20;
const long long mod = 1e9 + 7;
const long long inf = 1e18;
long long n, d[maxn], par[maxn][level];
long long lca(long long v, long long u) {
  if (d[v] < d[u]) swap(v, u);
  long long h = d[v] - d[u], z = 0;
  for (long long i = 0; i < level; i++) {
    if ((h >> i) & 1) {
      v = par[v][i];
      z += (1 << i);
    }
  }
  for (long long i = level - 1; i > -1; i--) {
    if (d[v] >= (1 << i) && par[v][i] != par[u][i]) {
      v = par[v][i];
      u = par[u][i];
      z += 2 * (1 << i);
    }
  }
  if (v != u) z += 2;
  return z;
}
int main() {
  long long v, u;
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n;
  v = u = 1;
  for (long long i = 2; i <= n; i++) {
    cin >> par[i][0];
    d[i] = d[par[i][0]] + 1;
    for (long long j = 1; j < level; j++) {
      if (d[i] >= (1 << j)) par[i][j] = par[par[i][j - 1]][j - 1];
    }
    if (lca(v, u) < max(lca(v, i), lca(u, i))) {
      if (lca(v, i) > lca(u, i))
        u = i;
      else
        v = i;
    }
    cout << lca(v, u) << ' ';
  }
  return 0;
}
