CF 253 Div1D

import java.io.*;
import java.util.*;

public class HLD {
    FastScanner in;
    PrintWriter out;

    class TwoMax {
        int val1, val2;

        TwoMax() {
            val1 = val2 = -1;
        }

        void addValue(int value) {
           if (value > val2) {
              val2 = value;
           }
            if (val2 > val1) {
                int tmp = val1;
                val1 = val2;
                val2 = tmp;
            }
        }
    }

    int res;
    int[] p;
    boolean[] isLayerTwo;
    int[] dp;
    TwoMax[] t;

    void update(int v) {
        if (isLayerTwo[v]) {
            res = Math.max(res, dp[v]);
            return;
        }
        t[p[v]].addValue(dp[v]);
        int newValue = Math.max(t[p[v]].val1, t[p[v]].val2 + 1);
        if (dp[p[v]] != newValue) {
            dp[p[v]] = newValue;
            update(p[v]);
        }
    }

    void solve() {
        int n = in.nextInt() + 1;
        p = new int[n];
        t = new TwoMax[n];
        isLayerTwo = new boolean[n];
        dp = new int[n];
        for (int i = 1; i < n; i++) {
            int parent = in.nextInt() - 1;
            if (parent == 0) {
                isLayerTwo[i] = true;
            } else {
                p[i] = parent;
            }
            t[i] = new TwoMax();
            dp[i] = 1;
            update(i);
            out.print(res + " ");
        }
    }

    void run() {
        try {
            in = new FastScanner(new File("object.in"));
            out = new PrintWriter(new File("object.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    public static void main(String[] args) {
        new HLD().runIO();
    }
}