A word of length n is "rich" if it contains, as subwords, exactly n distinct palindromes. You shoud find the number of binary rich words of length i for all i from 1 to n.
Input
The input contains an integer n (1 ≤ n ≤ 61).
Output
Sample
Problem Author: Mikhail Rubinchik
Problem Source: Palindromic Contest, July 11, 2015