Two rows of numbers

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 $y_1$ , …

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T12:00:39.323Z