Grid Puzzle I

There is an n \times n grid, and your task is to choose from each row and column some number of squares. How can you do that?

Input

The first input line has an integer n: the size of the grid. The rows and columns are numbered 1,2,\dots,n. The next line has n integers a_1,a_2,\ldots,a_n: You must choose exactly a_i squares from the ith row. The las line has n integers b_1,b_2,\ldots,b_n: You must choose exactly b_j squares from the jth column.

Output

Print n lines describing which squares you choose (X means that you choose a square, . means that you don't choose it). You can print any valid solution. If it is not possible to satisfy the conditions print only -1.

Constraints

$1 \le n \le 50$

$0 \le a_i \le n$

$0 \le b_j \le n$

Example

Input

5
0 1 3 2 0
1 2 2 0 1

Output

.....
..X..
.XX.X
XX...
.....