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We consider sequences of letters. We say a sequence x1,x2,…,xn contains a stammer, if we can find in it two occurrences of the same subsequence, one directly following the other, i.e. if for some i and j (1 ≤ i < j ≤ (n+i+1)/2) we have xi=xj, xi+1=xj+1,…,xj-1=x2j-i-1.
We are interested in n-element sequences having no stammers, built of the minimal number of different letters.
For n=3 it is enough to use two letters, say a and b. We have exactly two 3-element sequences without stammers build of those letters: aba and bab. For n=5 we need three different letters. For example abcab is a three-letter sequence without stammers. In the sequence babab we have two stammers: ba and ab.
Write a program which:
In the first line of the standard input there is one positive integer n, 1 ≤ n ≤ 10,000,000.
Your program should write to the standard output. In the first line there should be one positive integer k equal to the minimal number of different letters that must appear in an n-element sequence having no stammers.
In the second line one should write the computed sequence without stammers as a word that comprises n lower case letters of English alphabet and is built only of the letters from a up to the k-th letter of the alphabet. If there are many such sequences, your program should write one of them.
Olympiad > Polish Olympiad in Informatics > POI 2002/2003 > Stage 1 1번