Two rows of numbers P83712

You have $2n$ different numbers. Write a program to find all the ways to put the numbers in two rows $x_1 \dots x_n$ and $y_1 \dots y_n$ so that:

• $x_1 < x_2 < \dots < x_{n-1} < x_n$ ,

• $y_1 < y_2 < \dots < y_{n-1} < y_n$ ,

• for every $i$, it holds $x_i < y_i$.

Input

Input consists of $n$, followed by $2n$ different integer numbers. Assume $1 \le n \le 11$.

Output

Print all the ways to put the numbers fulfilling the required conditions. For every way, print three lines: two rows with $x_i$ and $y_i$ separated by spaces, and an empty line. Print the solutions in lexicographical order: first, those with the smaller $x_1$, in case of a tie, those with the smaller $x_2$, …, in case of a tie, those with the smaller $x_n$, in case of a tie, those with the smaller $y_1$, …