import java.util.*;
import java.lang.*;
 
class Main
{
    public static void countLevels(Integer tree[], int index, int levels[], int level)
    {
        if ( index >= tree.length )
            return;
 
        Integer node = tree[index];
 
        if ( node != null )
            levels[level] += 1;
 
        countLevels(tree, leftChild(index), levels, level+1);
        countLevels(tree, rightChild(index), levels, level+1);
    }
 
    public static int largestLevel(Integer tree[])
    {
        int levels[] = new int[numLevels(tree.length)];
        for (int x = 0; x < levels.length; x++)
            levels[x] = 0;
 
        countLevels(tree, 0, levels, 0);
 
        int max = -1;
        int maxLevel = -1;
 
        for (int level = 0; level < levels.length; level++)
        {
            if ( max < levels[level] )
            {
                max = levels[level];
                maxLevel = level;
            }
        }
 
        return maxLevel;
    }
 
    public static int numLevels(int nodeCount)
    {
        int log2 = (int) (Math.log(nodeCount+1)/Math.log(2));
        return log2;
    }
 
    public static int leftChild(int index)
        { return index*2 + 1; }
 
    public static int rightChild(int index)
        { return index*2 + 2; }
 
    public static void main (String[] args) throws java.lang.Exception
	{
		/* Given a binary tree return the level with maximum number of nodes
        0:        1
         :       / \
        1:      2   3
         :      /\  /\
        2:     4 5 6 7
         :    /       \
        3:   8         9 
           
           returns '2'
        */
 
        Integer e = null;
 
        System.out.println(
            largestLevel(new Integer[] { 
                        1, 
                2,              3, 
            4,      5,      6,      7, 
          8, e,    e, e,   e, e,   e, 9 } 
        ));
	}
}