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2037. Richness of binary words

Time limit: 0.5 second
Memory limit: 64 MB
For each integer i from 1 to n, you must print a string si of length n consisting of letters ‘a’ and ‘b’ only. The string si must contain exactly i distinct palindrome substrings. Two substrings are considered distinct if they are different as strings.

Input

The input contains one integer n (1 ≤ n ≤ 2000).

Output

You must print n lines. If for some i, the answer exists, print it in the form “i : si” where si is one of possible strings. Otherwise, print “i : NO”.

Sample

inputoutput
4
1 : NO
2 : NO
3 : NO
4 : aaaa
Problem Author: Mikhail Rubinchik
Problem Source: Ural FU Dandelion contest. Petrozavodsk training camp. Summer 2014