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 x₁ … x_n and y₁ … y_n so that:

• x₁ < x₂ < … < x_n−1 < x_n ,
• y₁ < y₂ < … < 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 ≤ n ≤ 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 x₁, in case of a tie, those with the smaller x₂, …, in case of a tie, those with the smaller x_n, in case of a tie, those with the smaller y₁, …