Largest Smallest Cyclic Shift

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.

Examples

Input

2 2 0

Output

abab

Input

1 1 1

Output

acb

inputFormat

Input

Input is given from Standard Input in the following format:

X Y Z

outputFormat

Output

Print the answer.

Examples

Input

2 2 0

Output

abab

Input

1 1 1

Output

acb

样例

2 2 0

abab