#include<bits/stdc++.h>

using namespace std;
#define int long long
int n, m, u, v, a[200005], subtree[200005], ans[200005];
multiset<int> mp[200005];
vector<int> adj[200005];
void build(int u, int par) {
	subtree[u] = 1;
	for (int node: adj[u]) {
		if(node == par) continue;
		build(node, u);
		subtree[u] += subtree[node];
	}
}
void dfs(int u, int par) {
	int mx=0, p=-1;
	for (int node: adj[u]) {
		if(node == par) continue;
		dfs(node, u);
		if(mx < subtree[node]) mx = subtree[node], p = node;
	}
	if(p==-1) {
		mp[u].insert(0);
		return;
	}
	int MAX = 0;
	vector<int> v;
	multiset<int> Q;
	Q.insert(*prev(mp[p].end()));
	for (int node: adj[u]) {
		if(node == par || node == p) continue;
		MAX = 0;
		Q.insert(*prev(mp[node].end()));
		if (Q.size() > 2) Q.erase(Q.begin());
		for (auto it: mp[node]) {
			mp[p].insert(it);
			MAX = max(MAX, it);
		}
		mp[node].clear();
	}
	swap(mp[p], mp[u]);
	if(Q.size() >= 2) {
		mp[u].insert(*Q.begin() + *next(Q.begin()) + 1);
		mp[u].erase(mp[u].lower_bound(*Q.begin())); 
		mp[u].erase(mp[u].lower_bound(*next(Q.begin())));
	}
}
void solve() {
	cin >> n;
	for (int i = 2; i <= n; i++) {
		cin >> u; v = i;
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	cout << '\n';
	int cnt = 0;
	for (int i = 1; i <= n; i++) cnt += (adj[i].size()==1 && i != 1 ? 1 : 0);
	build(1, -1);
	dfs(1,-1);
	int sl = 0;
	ans[1] = 1;
	for (auto i = mp[1].rbegin(); i != mp[1].rend(); i++) {
		int num = *i;
		cout << num << ' ';
		for (int j = 0; j <= num; j++) ans[sl+1+j] = ans[sl]+1+2*j;
		sl += 1 + num;
	}
	cout << '\n';
	for (int i = 1; i <= cnt; i++) cout << ans[i] << ' ';
}

signed main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	if(fopen("input.inp","r")){
		freopen("input.inp", "r", stdin);
		freopen("output.out", "w", stdout);
	}
	int t = 1;
	// cin >> t;
	while(t--) {
		solve();
	}
}//