#include<bits/stdc++.h>
using namespace std ;
typedef long long ll ;
typedef unsigned long long ull ;
typedef pair < int , int > pii ;
typedef vector < int > vi ;
#define fi first
#define se second
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()

const int MAXN = 2e5 + 7 ;
const int LOG = 20 ;

int n , k ;
vector < int > v[ MAXN ] ;
int dp[ MAXN ] , nxt[ MAXN ][ 2 ] ;
int prv[ MAXN ] ;

void dfs ( int x ) {
    vector < pii > srt ;
    for ( auto y : v[ x ] ) {
        dfs ( y ) ;
        srt.push_back ( { dp[ y ] , y } ) ;
    }
    int sz = v[ x ].size ( ) ;
    if ( sz == 0 ) {
        ++ k ;
        return ;
    }
    if ( sz == 1 ) {
        dp[ x ] = srt[ 0 ].fi ;
        nxt[ x ][ 0 ] = srt[ 0 ].se ;
        return ;
    }
    sort ( srt.begin ( ) , srt.end ( ) , greater < pii > ( ) ) ;
    dp[ x ] = srt[ 0 ].fi + srt[ 1 ].fi ;
    nxt[ x ][ 0 ] = srt[ 0 ].se , nxt[ x ][ 1 ] = srt[ 1 ].se ;
    ++ dp[ x ] ;
}

int ans[ MAXN ] ;

void solve ( ) {
    cin >> n ;
    for ( int i = 2 , x ; i <= n ; ++ i ) {
        cin >> x ;
        prv[ i ] = x ;
        v[ x ].push_back ( i ) ;
    }
    dfs ( 1 ) ;
    vector < int > srt ;
    for ( int i = 1 ; i <= n ; ++ i ) {
        if ( nxt[ prv[ i ] ][ 0 ] != i && nxt[ prv[ i ] ][ 1 ] != i ) {
            srt.push_back ( dp[ i ] ) ;
        }
    }
    sort ( srt.begin ( ) , srt.end ( ) ) ;
    int tp = 1 ;
    ans[ 1 ] = 0 ;
    while ( srt.empty ( ) == false ) {
        int aux = srt.back ( ) ;
        srt.pop_back ( ) ;
        while ( aux > 0 && tp < k ) {
            ++ tp , -- aux ;
            ans[ tp ] = ans[ tp - 1 ] + 1 ;
        }
        ++ tp ;
        ans[ tp ] = ans[ tp - 1 ] ;
    }
    while ( tp < k ) {
        ++ tp ;
        ans[ tp ] = ans[ tp - 1 ] ;
    }
    for ( int i = 1 ; i <= k ; ++ i ) {
        ans[ i ] += i ;
        printf ( "%d " , ans[ i ] ) ;
    }
    printf ( "\n" ) ;
}

int main ( ) {
    ios_base :: sync_with_stdio ( false ) ;
    cin.tie ( NULL ) ;
    int t = 1 ; // cin >> t ;
    while ( t -- ) { solve ( ) ; }
    return 0 ;
}