#include <bits/stdc++.h>
using namespace std;

// Returns maximum leaves in a subtree that can achieve the largest possible LCA set.
int dfs(vector<vector<int>> &tree, int cur) {
    vector<int> max_leaves;
    for (int child : tree[cur]) {
        max_leaves.push_back(dfs(tree, child));
    }
    sort(max_leaves.begin(), max_leaves.end());

    if (max_leaves.size() == 0) {
        return 1;
    } else if (max_leaves.size() == 1) {
        return max_leaves[0];
    } else {
        int size = max_leaves.size();
        return max_leaves[size - 1] + max_leaves[size - 2];
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n;
    cin >> n;
    vector<vector<int>> tree(n);
    for (int i = 1; i < n; i++) {
        int pi;
        cin >> pi;
        tree[pi - 1].push_back(i);
    }
    int leaf_cnt = 0;
    for (int i = 1; i < n; i++) {
        if (tree[i].size() == 0) {
            leaf_cnt++;
        }
    }
    
    int max_leaves = dfs(tree, 0);
    int res = 1;
    for (int i = 1; i <= leaf_cnt; i++) {
        cout << res << " ";
        if (i < max_leaves) {
            res += 2;
        } else {
            res++;
        }
    }
    cout << "\n";
}