We consider sequences of letters. We say a sequence $x_1,x_2,…,x_n$ 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 $j$ ($1 ≤ i < j ≤ \frac{n+i+1}{2}$) 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
Write a program which:
- 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 $n$, $1 ≤ n ≤ 10,000,000$.
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.
Example
Input
5
Output
3 abcab