A snake fills a 3xn board completely. Successive segments of the snake are numbered from 1 to 3n. The segments with successive numbers (i.e., 1 and 2, 2 and 3, 3 and 4...) occupy squares that share an edge. For example, a snake can fill a 3x9 board as follows:</p>

The snake's segment numbers in some of the squares have been erased. Can you reconstruct the snake?

입력 형식

In the first line of the standard input, there is a single integer n (1 ≤ n ≤ 1,000), the length of the board. The three lines that follow describe the board; the i-th of them contains n integers a_ij (0 ≤ a_ij ≤ 3n for 1 ≤ j ≤ n). If a_ij > 0, then a_ij is the number of the snake's segment occupying the j-th square of the i-th row of the board. If on the other hand a_ij=0, then the number of the snake's segment on this square is unknown.

출력 형식

Your program is to print three lines to the standard output. The i-th lines should hold n positive integers b_ij(for 1 ≤ j ≤ n). All the numbers b_ij together should be a permutation of the numbers from 1 to 3n. The output numbers should be a valid reconstruction of the snake, i.e., they should be consistent with the (positive) input numbers and satisfy aforementioned constraints.</p>

You may assume that there is at least one valid reconstruction of the snake. If there is more than one, your program can print any valid reconstruction.

예제 입력

9
0 0 5 0 17 0 0 0 21
8 0 0 3 16 0 0 25 0
0 0 0 0 0 0 0 0 23

예제 출력

7 6 5 4 17 18 19 20 21
8 1 2 3 16 15 26 25 22
9 10 11 12 13 14 27 24 23