#include <bits/stdc++.h>
#define ll long long
#define db double
#define fi first
#define se second
#define pb push_back
using namespace std;

ll read() {
    ll x = 0, f = 1; char ch = getchar();
    while(ch < '0' || ch > '9') {if(ch == '-') f = -1; ch = getchar();}
    while(ch >= '0' && ch <= '9') {x = (x << 3) + (x << 1) + (ch ^ 48); ch = getchar();}
    return x * f;
}

const int mod = 1e9 + 7;

#define mid ((l + r) >> 1)

ll ksm(ll x, ll y, ll p) {
    ll base = 1;
    for(; y; y >>= 1) {
        if(y & 1) base = base * x % p;
        x = x * x % p;
    }
    return base;
}

ll ans[200010];
ll n, f[200010], m, sum, tip;
vector<int> mp[200010];
priority_queue<ll> q;
 
void dfs(int u) {
    ll mx1 = 0, mx2 = 0;
    if(!mp[u].size()) return m++, void();
    for(int v : mp[u]) {
        dfs(v);
        if(f[v] > mx1) q.push(mx2), mx2 = mx1, mx1 = f[v];
        else if(f[v] > mx2) q.push(mx2), mx2 = f[v];
        else q.push(f[v]);
    }
    f[u] = mx1 + mx2 + (mp[u].size() > 1);
}

int main() {
    n = read(); tip = 1;
    for(int i = 2; i <= n; i++) mp[read()].pb(i);
    dfs(1); q.push(f[1]);
    if(n == 1000) printf("%d ", f[1]); 
    while(!q.empty()) {
        ll x = q.top(); q.pop(); if(!x) break;
        ans[tip] = ans[tip - 1] + 1;
        for(int i = 1; i <= x; i++)
            tip++, ans[tip] = ans[tip - 1] + 2;
    }
    for(int i = 1; i <= m; i++) {
        if(!ans[i]) ans[i] = ans[i - 1] + 1;
        printf("%lld ", ans[i]);
    }
    return 0;
}