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 inf = 1 << 28;
const int mod = (int)1e6 + 3;
int n, m, k;
vector<int> e[200010];
int dp[200010][20];
int dep[200010];
void dfs(int u, int fa) {
  dp[u][0] = fa;
  dep[u] = dep[fa] + 1;
  for (int i = 1; i <= 19; i++) dp[u][i] = dp[dp[u][i - 1]][i - 1];
  for (auto v : e[u]) dfs(v, u);
}
int lca(int u, int v) {
  if (dep[u] < dep[v]) swap(u, v);
  for (int i = 0, det = dep[u] - dep[v]; i <= 19; i++)
    if (det & (1 << i)) u = dp[u][i];
  if (u == v) return u;
  for (int i = 19; i >= 0; i--) {
    if (dp[u][i] == dp[v][i]) continue;
    u = dp[u][i];
    v = dp[v][i];
  }
  return dp[u][0];
}
int main() {
  cin >> n;
  int x;
  for (int i = 2; i <= n; i++) {
    scanf("%d", &x);
    e[x].push_back(i);
  }
  dfs(1, 0);
  int u = 1, v = 1, len = 0;
  for (int i = 2; i <= n; i++) {
    int x = lca(i, u), len1 = dep[i] + dep[u] - 2 * dep[x];
    int y = lca(i, v), len2 = dep[i] + dep[v] - 2 * dep[y];
    if (len1 > len) len = len1, v = u, u = i;
    if (len2 > len) len = len2, u = v, v = i;
    printf("%d%c", len, i == n ? '\n' : ' ');
  }
  return 0;
}
