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Palindromic Contest

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E. OEIS A216264

Time limit: 1.0 second
Memory limit: 64 MB
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

Output n integers.

Sample

inputoutput
4
2
4
8
16
Problem Author: Mikhail Rubinchik
Problem Source: Palindromic Contest, July 11, 2015
To submit the solution for this problem go to the Problem set: 2061. OEIS A216264