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...
.....