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 $i$th row.

The las line has $n$ integers $b_1,b_2,\ldots,b_n$: You must choose exactly $b_j$ squares from the $j$th 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...
.....