#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, vector<int> &unadded, int cur) {
    vector<int> max_leaves;
    for (int child : tree[cur]) {
        max_leaves.push_back(dfs(tree, unadded, 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();
        for (int i = 0; i < size - 2; i++) {
            unadded.push_back(max_leaves[i]);
        }
        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++;
        }
    }
    
    vector<int> unadded;
    int max_leaves = dfs(tree, unadded, 0);
    sort(unadded.begin(), unadded.end());
    int p = unadded.size() - 1;
    
    vector<int> res(leaf_cnt + 1);
    res[1] = 1;
    for (int i = 2; i <= max_leaves; i++) {
        res[i] = res[i - 1] + 2;
    }

    int ind = max_leaves + 1;
    while (p >= 0 && ind <= leaf_cnt) {
        res[ind] = res[ind - 1] + 1;
        ind++;
        for (int i = 0; i < unadded[p]; i++) {
            if (ind > leaf_cnt) {
                break;
            }
            res[ind] = res[ind - 1] + 2;
            ind++;
        }
        p--;
    }
    while (ind <= leaf_cnt) {
        res[ind] = res[ind - 1] + 1;
        ind++;
    }

    for (int i = 1; i <= leaf_cnt; i++) {
        cout << res[i] << " ";
    }
    cout << "\n";
}