// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
//#define int long long
#define ull unsigned long long
using namespace std;
inline int read()
{
    char c=getchar();int x=0;bool f=0;
    for(;!isdigit(c);c=getchar())f^=!(c^45);
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
    if(f)x=-x;return x;
}


#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,int b){return a.x==b;}
	friend bool operator !=(modint a,int b){return a.x!=b;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;
 
#define maxn 300005
#define inf 0x3f3f3f3f

//std::string trans(int s) { return s ? trans(s >> 1) + char('0' | (s & 1)) : ""; }
//std::string f(std::string c)
//{
//    std::string res;
//    for (std::size_t i = 0, j = 0; i != c.size(); i = j)
//    {
//        while (j != c.size() && c[i] == c[j])
//            ++j;
//        res += trans(j - i) + c[i];
//  //      std::cout<<j-i<<" ";
//    }
//    std::cout<<std::endl;
//    return res;
//}
//
//string s[]

int n,fa[maxn];
vi e[maxn];
int sz[maxn],f[maxn];
int all=0;

priority_queue<int>q[maxn];
void dfs(int u){
	if(e[u].empty()){
		q[u].push(0);
		return;
	}
	vi tmp;
	for(int v:e[u]){
		dfs(v);
		tmp.pb(q[v].top()),q[v].pop();
		if(q[u].size()<q[v].size())swap(q[u],q[v]);
		while(q[v].size())q[u].push(q[v].top()),q[v].pop();	
	}
	if(e[u].size()==1){
		for(int x:tmp) q[u].push(x);
		return;
	}
	sort(tmp.begin(),tmp.end(),greater<int>());
	int x=tmp[0],y=tmp[1];
	q[u].push(x+y+1);
	For(i,2,(int)tmp.size()-1) q[u].push(tmp[i]);
}

signed main()
{
	n=read();
	For(i,2,n)fa[i]=read(),e[fa[i]].pb(i);
	dfs(1);
	int res=0;
	vi o;
	while(q[1].size()){
		res+=1,o.pb(res);
		int x=q[1].top();q[1].pop();
		while(x--)res+=2,o.pb(res);
	}
	for(auto x:o)cout<<x<<" ";
	return 0;
}
/*

*/