#include <bits/stdc++.h>
using namespace std;
const int N = 500005 , LG = 20;

struct node
{
	int to , val , nxt;
} e[ N << 1 ];
int head[ N ] , tot = 0;
int d[ N ];
int f[ N ][ LG ];

int n;

void add_edge( int from , int to )
{
	e[ ++ tot ] = node{ to , head[ from ] };
	head[ from ] = tot;
}

void add_fa( int u , int fa )
{
	d[ u ] = d[ fa ] + 1;
	f[ u ][ 0 ] = fa;

	for( int i = 1 ; i <= 19 ; i ++ )
		f[ u ][ i ] = f[ f[ u ][ i - 1 ] ][ i - 1 ];
}

int lca( int x , int y )
{
	if( d[ x ] < d[ y ] ) // 确保dx>=dy 
		x ^= y ^= x ^= y;

	for( int i = 19 ; i >= 0 ; i -- )
		if( d[ f[ x ][ i ] ] >= d[ y ] )
			x = f[ x ][ i ];

	if( x == y )
		return x;

	for( int i = 19 ; i >= 0 ; i -- )
		if( f[ x ][ i ] != f[ y ][ i ] )
			x = f[ x ][ i ] , y = f[ y ][ i ];

	return f[ x ][ 0 ];
}

int len( int x , int y )
{
	int l = lca( x , y );
	return d[ x ] + d[ y ] - 2 * d[ l ];
}

int main() 
{
	cin >> n;

	int st = 1 , ed = 1;
	for( int i = 2 , p ; i <= n ; i ++ )
	{
		cin >> p;
		add_edge( p , i );
		add_fa( i , p );
	
		if( len( st , ed ) < len( st , i ) || len( st , ed ) < len( i , ed ) )
		{
			if( len( st , i ) < len( i , ed ) )
				st = i;
			else
				ed = i;
		}
	
		cout << len( st , ed ) << " ";
	}
	return 0;
}