#include <bits/stdc++.h>
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define st first
#define nd second
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
const int N = 1e6 + 5;
vector<int> adj[N];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	int n; cin >> n;
	for (int i = 1, p; i < n; i++) {
		cin >> p;
		p--;
		adj[p].push_back(i);
	}
	vector<vector<int>> dp(n);
	for (int i = n - 1; i >= 0; i--) {
		dp[i] = {0};
		if (adj[i].empty()) {
			dp[i].push_back(1);
			continue;
		}
		vector<array<int, 2>> a(1);
		a[0] = {0, 0};
		for (int j: adj[i]) {
			vector<array<int, 2>> nx(size(a) + size(dp[j]) - 1);
			for (int k = 0; k < size(a); k++)
				for (int kk = 0; kk < size(dp[j]); kk++)
					for (int l = 0; l < 2; l++)
						nx[k + kk][l | (k > 0 && kk > 0)] = max(nx[k + kk][l | (k > 0 && kk > 0)], a[k][l] + dp[j][kk] + (l == 0 && k > 0 && kk > 0));
			swap(a, nx);
		}
		dp[i].resize(size(a));
		for (int k = 0; k < size(a); k++)
			dp[i][k] = max(a[k][0], a[k][1]);
	}
	for (int i = 1; i < size(dp[0]); i++)
		cout << dp[0][i] << " ";
	cout << "\n";
}