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 mod = 1000000007;
const int inf = 50000000;
const int maxn = 200010;
const int logn = 21;
vector<int> adj[maxn];
int n, p[maxn], dp[logn][maxn], depth[maxn];
void dfs(int cur, int parent, int d) {
  depth[cur] = d;
  dp[0][cur] = parent;
  for (int it : adj[cur]) {
    if (it != parent) {
      dfs(it, cur, d + 1);
    }
  }
}
int LCA(int u, int v) {
  if (depth[u] > depth[v]) swap(u, v);
  int i, diff = depth[v] - depth[u];
  for (i = logn - 1; i >= 0; i--) {
    if (diff & (1 << i)) v = dp[i][v];
  }
  for (i = logn - 1; i >= 0; i--) {
    if (dp[i][u] != dp[i][v]) {
      u = dp[i][u];
      v = dp[i][v];
    }
  }
  if (u == v) return u;
  return dp[0][u];
}
int distance(int u, int v) {
  int lca = LCA(u, v);
  int dist = depth[u] + depth[v] - 2 * depth[lca];
  return dist;
}
int main() {
  scanf("%d", &n);
  int i, j;
  for (i = 2; i <= n; i++) {
    scanf("%d", &p[i]);
    adj[p[i]].push_back(i);
    adj[i].push_back(p[i]);
  }
  dfs(1, 0, 0);
  for (i = 1; i < logn; i++) {
    for (j = 1; j <= n; j++) dp[i][j] = dp[i - 1][dp[i - 1][j]];
  }
  int u, v, d1, d2, d3;
  u = v = 1;
  for (i = 2; i <= n; i++) {
    d1 = distance(u, v);
    d2 = distance(u, i);
    d3 = distance(v, i);
    if (max(d2, d3) > d1) {
      d1 = max(d2, d3);
      if (d2 == d1)
        v = i;
      else
        u = i;
    }
    printf("%d ", d1);
  }
  printf("\n");
  return 0;
}
