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 N = 2e5 + 9;
const int LOG = 18;
vector<int> g[N];
int dp[LOG][N];
int depth[N];
int get_dist(int u, int v) {
  if (depth[u] > depth[v]) swap(u, v);
  int ret = depth[u] + depth[v];
  for (int i = LOG - 1; i >= 0; --i)
    if (depth[v] - depth[u] >= (1 << i)) v = dp[i][v];
  if (u == v) return ret - 2 * depth[v];
  for (int i = LOG - 1; i >= 0; --i)
    if (dp[i][v] != dp[i][u]) {
      v = dp[i][v];
      u = dp[i][u];
    }
  u = v = dp[0][v];
  return ret - 2 * depth[v];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  int a, b;
  a = b = 1;
  int dist = 0;
  for (int i = 0; i < LOG; ++i) dp[i][1] = 1;
  for (int v = 2; v <= n; ++v) {
    int par;
    cin >> par;
    dp[0][v] = par;
    depth[v] = depth[par] + 1;
    for (int i = 1; i < LOG; ++i) dp[i][v] = dp[i - 1][dp[i - 1][v]];
    if (get_dist(a, v) < get_dist(b, v)) swap(a, b);
    if (get_dist(a, v) > dist) {
      dist = get_dist(a, v);
      b = v;
    }
    cout << dist << "\n";
  }
}
