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;
int break_point() {
  char c;
  while ((c = getchar()) != '\n')
    ;
  return 0;
}
template <typename T>
void read_integer(T &r) {
  bool sign = 0;
  r = 0;
  char c;
  while (1) {
    c = getchar();
    if (c == '-') {
      sign = 1;
      break;
    }
    if (c != ' ' && c != '\n') {
      r = c - '0';
      break;
    }
  }
  while (1) {
    c = getchar();
    if (c == ' ' || c == '\n') break;
    r = r * 10 + (c - '0');
  }
  if (sign) r = -r;
}
long long binpowmod(long long a, long long b, long long mod) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      res %= mod;
      b--;
    } else {
      a *= a;
      a %= mod;
      b >>= 1;
    }
  }
  return res;
}
long long binpow(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      b--;
    } else {
      a *= a;
      b >>= 1;
    }
  }
  return res;
}
inline int getbit(int x, int b) { return (x >> b) & 1; }
inline long long getbit(long long x, int b) { return (x >> b) & 1; }
inline unsigned long long getbit(unsigned long long x, int b) {
  return (x >> b) & 1;
}
inline int setbit(int x, int b) { return x | (1 << b); }
inline void _setbit(int &x, int b) { x = setbit(x, b); }
inline long long setbit(long long x, int b) { return x | (1ll << b); }
inline void _setbit(long long &x, int b) { x = setbit(x, b); }
inline int unsetbit(int x, int b) { return x & (INT_MAX - (1 << b)); }
inline void _unsetbit(int &x, int b) { x = unsetbit(x, b); }
inline int countbit(int x) {
  x = x - ((x >> 1) & 0x55555555);
  x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
  return ((x + (x >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
}
inline long long countbit(long long x) {
  int p1 = (x >> 32) & ((1ll << 32) - 1);
  int p2 = x & ((1ll << 32) - 1);
  return countbit(p1) + countbit(p2);
}
template <typename T>
void printbit(T x, int len) {
  for (int i = len - 1; i >= 0; i--) printf("%d", getbit(x, i));
}
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
template <typename A, typename B>
ostream &operator<<(ostream &stream, const pair<A, B> &p) {
  stream << "{" << p.first << "," << p.second << "}";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const vector<A> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A, typename B>
ostream &operator<<(ostream &stream, const map<A, B> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const set<A> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const stack<A> &v) {
  stack<A> st = v;
  stream << "[";
  while (!st.empty()) {
    stream << st.top() << " ";
    st.pop();
  }
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const priority_queue<A> &v) {
  priority_queue<A> q = v;
  stream << "[";
  while (!q.empty()) {
    stream << q.top() << " ";
    q.pop();
  }
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const queue<A> &v) {
  queue<A> q = v;
  stream << "[";
  while (!q.empty()) {
    stream << q.front() << " ";
    q.pop();
  }
  stream << "]";
  return stream;
}
void run();
int main() {
  srand(time(NULL));
  do {
    run();
    if (0) {
      0 ? printf("-------------------------------\n") : 0;
      0 ? printf("-------------------------------\n") : 0;
      0 ? break_point() : 0;
    }
  } while (0);
  return 0;
}
const int mod = 1e6 + 3;
const int N = 200005;
int in[N], out[N], TM;
int dp[N][25];
int pr[N];
int res[N];
int d[N];
vector<int> g[N];
void dfs(int v, int p = 1) {
  in[v] = TM++;
  dp[v][0] = p;
  for (int i = 1; i < 20; ++i) dp[v][i] = dp[dp[v][i - 1]][i - 1];
  for (int to : g[v]) {
    if (to == p) continue;
    d[to] = d[v] + 1;
    dfs(to, v);
  }
  out[v] = TM++;
}
bool isAncestor(int a, int b) { return in[a] <= in[b] && out[a] >= out[b]; }
int lca(int a, int b) {
  if (isAncestor(a, b)) return a;
  if (isAncestor(b, a)) return b;
  for (int i = 19; i >= 0; --i)
    if (!isAncestor(dp[a][i], b)) a = dp[a][i];
  return dp[a][0];
}
int dist(int a, int b) {
  int c = lca(a, b);
  return d[a] + d[b] - 2 * d[c];
}
void run() {
  int n;
  scanf("%d", &n);
  for (int i = 2; i <= n; ++i) {
    scanf("%d", &pr[i]);
    g[i].push_back(pr[i]);
    g[pr[i]].push_back(i);
  }
  dfs(1);
  int x = 1, y = g[1][0];
  res[2] = 1;
  0 ? (cout << "x"
            << " = " << (x) << ","
            << "y"
            << " = " << (y) << "\n")
    : cout << "";
  for (int i = 3; i <= n; ++i) {
    int c = dist(i, x) > dist(i, y) ? x : y;
    if (dist(x, y) < dist(i, c)) x = i, y = c;
    res[i] = dist(x, y);
    0 ? (cout << "i"
              << " = " << (i) << ","
              << "x"
              << " = " << (x) << ","
              << "y"
              << " = " << (y) << "\n")
      : cout << "";
  }
  for (int i = 2; i <= n; ++i) printf("%d ", res[i]);
  putchar('\n');
}
