// 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define debug(...) fprintf (stderr, __VA_ARGS__)

#define lep(i, l, r) for (int i = (l), i##_end = (r); i <= i##_end; ++ i)
#define rep(i, r, l) for (int i = (r), i##_end = (l); i >= i##_end; -- i)

char _c; bool _f; template <class T> inline void IN (T & x) {
	_f = 0, x = 0; while (_c = getchar (), ! isdigit (_c)) if (_c == '-') _f = 1;
	while (isdigit (_c)) x = x * 10 + _c - '0', _c = getchar (); if (_f) x = - x;
}

const int N = 2e5 + 5;

int n, leaf, dp[N];
vector <int> to[N];

vector <int> stk;
void dfs (int u) {
	if (! to[u].size ()) {
		dp[u] = 1, ++ leaf;
	} else if (to[u].size () == 1) {
		dfs (to[u][0]);
		dp[u] = dp[to[u][0]];
	} else {
		for (auto & v : to[u]) dfs (v);
		sort (to[u].begin (), to[u].end (), [&] (int a, int b) { return dp[a] > dp[b]; });
		dp[u] = dp[to[u][0]] + dp[to[u][1]];
		lep (i, 2, to[u].size () - 1) stk.emplace_back ( dp[to[u][i]] );
	}
}

signed main () {
	IN (n);
	for (int p, i = 2; i <= n; ++ i) IN (p), to[p].emplace_back ( i );
	dfs (1), stk.emplace_back ( dp[1] );

	vector <int> tag (leaf + 2);
	sort (stk.begin (), stk.end (), greater <int> ());
	{
		int p = 0;
		for (auto & x : stk) if (x > 1) {
			++ tag[p + 2];
			-- tag[p + x + 1];
			p += x;
		}
		lep (i, 1, leaf) tag[i] += tag[i - 1];
	}
	int ans = 0;
	lep (i, 1, leaf) ++ ans, ans += tag[i], printf ("%d%c", ans, " \n"[i == n]);
	return 0;
}