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>
#pragma comment(linker, "/STACK:667772160")
using namespace std;
struct __isoff {
  __isoff() {
    if (0) freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
    srand('C' + 'T' + 'A' + 'C' + 'Y' + 'M' + 'B' + 'A');
  }
  ~__isoff() {}
} __osafwf;
const unsigned long long p1 = 31;
const unsigned long long p2 = 29;
const double eps = 1e-8;
const double pi = acos(-1.0);
const int infi = 1e9 + 7;
const long long inf = 1e18 + 7;
const long long dd = 2e5 + 7;
const long long mod = 1e9 + 7;
const int logc = 20;
int up[dd][logc], H[dd], in[dd], out[dd], ti = 0;
vector<int> P[dd];
void dfs(int v, int p = 0, int h = 0) {
  H[v] = h;
  in[v] = ti++;
  up[v][0] = p;
  for (int i = 1; i < logc; i++) {
    up[v][i] = up[up[v][i - 1]][i - 1];
  }
  for (auto it : P[v]) {
    if (it != p) {
      dfs(it, v, h + 1);
    }
  }
  out[v] = ti++;
}
void build() { dfs(0); }
bool is(int a, int b) { return in[a] <= in[b] && out[b] <= out[a]; }
int lca(int a, int b) {
  if (is(a, b)) {
    return a;
  }
  if (is(b, a)) {
    return b;
  }
  for (int i = logc - 1; i >= 0; i--) {
    int t = up[a][i];
    if (!is(t, b)) {
      a = t;
    }
  }
  return up[a][0];
}
int dis(int a, int b) { return H[a] + H[b] - 2 * H[lca(a, b)]; }
int main() {
  int n;
  cin >> n;
  vector<int> E;
  for (long long i = 0; i < (long long)n - 1; i++) {
    int t;
    cin >> t;
    t--;
    P[t].push_back(i + 1);
    E.push_back(i + 1);
  }
  build();
  int a = 0, b = 0, l = 0;
  for (long long i = 0; i < (long long)n - 1; i++) {
    int t = E[i];
    if (l < dis(a, t)) {
      l = dis(a, t);
      b = t;
    }
    if (l < dis(b, t)) {
      l = dis(b, t);
      a = t;
    }
    cout << l << '\n';
  }
}
