//Author: Kevin
#include<bits/stdc++.h>
//#pragma GCC optimize("O2")
using namespace std;
#define ll long long
#define ull unsigned ll
#define pb emplace_back
#define mp make_pair
#define ALL(x) (x).begin(),(x).end()
#define rALL(x) (x).rbegin(),(x).rend()
#define srt(x) sort(ALL(x))
#define rev(x) reverse(ALL(x))
#define rsrt(x) sort(rALL(x))
#define sz(x) (int)(x.size())
#define inf 0x3f3f3f3f
#define pii pair<int,int>
#define lb(v,x) (int)(lower_bound(ALL(v),x)-v.begin())
#define ub(v,x) (int)(upper_bound(ALL(v),x)-v.begin())
#define uni(v) v.resize(unique(ALL(v))-v.begin())
#define longer __int128_t
void die(string S){puts(S.c_str());exit(0);}
int n;
int anc[20][200200];
int depth[200200];
int lca(int u,int v)
{
	for(int i=19;i>=0;i--)
	{
		if(depth[anc[i][u]]>=depth[v])
			u=anc[i][u];
		if(depth[anc[i][v]]>=depth[u])
			v=anc[i][v];
	}
	if(u==v) return u;
	for(int i=19;i>=0;i--)
		if(anc[i][u]!=anc[i][v])
		{
			u=anc[i][u];
			v=anc[i][v];
		}
	return anc[0][u];
}
bool isleaf[200200];
int dfn[200200],tot;
vector<int> G[200200];
void dfs(int u)
{
	dfn[u]=++tot;
	for(auto v:G[u])
		dfs(v);
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(int i=2;i<=n;i++)
		cin>>anc[0][i];
	for(int i=1;i<20;i++)
		for(int j=1;j<=n;j++)
			anc[i][j]=anc[i-1][anc[i-1][j]];
	for(int i=1;i<=n;i++)
	{
		G[anc[0][i]].pb(i);
		isleaf[anc[0][i]]=true;
		depth[i]=depth[anc[0][i]]+1;
	}
	vector<int> vec;
	for(int i=1;i<=n;i++)
		if(!isleaf[i])
			vec.pb(i);
	sort(ALL(vec),[&](const int &a,const int &b){return dfn[a]<dfn[b];});
	int ans=0;
	vector<int> st;
	for(auto x:vec)
	{
		if(!sz(st))
		{
			st.pb(x);
			continue;
		}
		int a=lca(x,st.back());
		while(sz(st)>1&&depth[a]<depth[st[sz(st)-2]])
		{
			ans++;
			st.pop_back();
		}
		if(depth[a]<depth[st.back()])
		{
			ans++;
			st.pop_back();
		}
		if(!sz(st)||st.back()!=a)
			st.pb(a);
		st.pb(x);
	}
	ans+=sz(st);
	ans-=sz(vec);
	int val=-1;
	ans++;
	for(int i=0;i<sz(vec);i++)
	{
		val++;
		if(ans>0) val++;
		ans--;
		cout<<val<<" ";
	}
	return 0;
}