Score : $1600$ points

Problem Statement

For a string $S$, let $f(S)$ be the lexicographically smallest cyclic shift of $S$. For example, if $S =$babca, $f(S) =$ababc because this is the smallest among all cyclic shifts (babca, abcab, bcaba, cabab, ababc).

You are given three integers $X, Y$, and $Z$. You want to construct a string $T$ that consists of exactly $X$ as, exactly $Y$ bs, and exactly $Z$ cs. If there are multiple such strings, you want to choose one that maximizes $f(T)$ lexicographically.

Compute the lexicographically largest possible value of $f(T)$.

Constraints

• $1 \leq X + Y + Z \leq 50$
• $X, Y, Z$ are non-negative integers.

Input

Input is given from Standard Input in the following format:

$X$ $Y$ $Z$

Output

Print the answer.

2 2 0

abab

$T$ must consist of two as and two bs.

• If $T =$aabb, $f(T) =$aabb.
• If $T =$abab, $f(T) =$abab.
• If $T =$abba, $f(T) =$aabb.
• If $T =$baab, $f(T) =$aabb.
• If $T =$baba, $f(T) =$abab.
• If $T =$bbaa, $f(T) =$aabb.

Thus, the largest possible $f(T)$ is abab.

1 1 1

acb