**Time limit:**1.00 s**Memory limit:**512 MB

**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...

.....