We consider sequences of letters. We say a sequence x₁x₂...x_n 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 x_i = x_j, x_i+1 = x_j+1, ..., x_j-1 = x_2j-i-1.

We are interested in n-element sequences having no stammers, built of the minimal number of different letters.

Example

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.

Task

• reads the length of the sequence n,
• computes an n-element sequence with no stammers built of the minimal number of different letters,
• writes the result.

Input

In the first line of the standard input there is one positive integer n, 1 <= n <= 10000000.

Output

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.

You may assume 26 letters are enough.

Example

5

3
abcab

Print friendly version