Problem Statement

You are given a triple of positive integers $(X,Y,Z)$ such that $X\leq Y\leq Z$.

Output one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions:

• The lengths of $S_1,S_2,S_3$ are each between $1$ and $1000$, inclusive.
• The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_2$ is $X$.
• The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_3$ is $Y$.
• The length of a longest sequence that is both a contiguous subsequence of $S_2$ and a contiguous subsequence of $S_3$ is $Z$.
• $\max(\max(S_1),\max(S_2),\max(S_3))$ is minimized among all triples satisfying the above four conditions.

It can be proved that under the constraints of this problem, a triple $(S_1,S_2,S_3)$ satisfying the conditions always exists. If there are multiple such triples, you may output any of them.

Constraints

• $1\leq X\leq Y\leq Z\leq 100$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

X Y Z

Output

Output three lines.

The first line should contain $S_1$ in the following format, where $|S_1|$ denotes the length of $S_1$ and $S_{1,i}$ denotes the $i$-th element of $S_1$:

|S_1| S_{1,1} S_{1,2} \dots S_{1,|S_1|}

The second line should contain $S_2$ and the third line should contain $S_3$, both in the same format as $S_1$.

If there are multiple solutions, you may output any of them.