Problem Statement

There is an $H \times W$ grid. The square in the $i$-th row from the top and the $j$-th column from the left is denoted by $(i, j)$; in particular, the top-left square is $(1, 1)$.
Among the $HW$ squares, $K$ squares have houses built on them, located at squares $(x_1, y_1)$, $(x_2, y_2)$, ..., $(x_K, y_K)$.
E869120 wants to choose, for each square without a house, whether to plant $1$ tree on it, so that the following conditions are satisfied.

• In row $i$ $(1 \leq i \leq H)$, exactly $A_i$ trees are planted in total.
• In column $j$ $(1 \leq j \leq W)$, exactly $B_j$ trees are planted in total.

Input

$H$ $W$
$A_1$ $A_2$ $A_3$ ... $A_H$
$B_1$ $B_2$ $B_3$ ... $B_W$
$K$
$x_1$ $y_1$
$x_2$ $y_2$
$x_3$ $y_3$
: :
$x_K$ $y_K$

The $1$st line contains integers $H$, $W$, separated by spaces.
The $2$nd line contains integers $A_1$, $A_2$, ..., $A_H$, separated by spaces.
The $3$rd line contains integers $B_1$, $B_2$, ..., $B_W$, separated by spaces.
The $4$th line contains an integer $K$.
The $5+i$-th $(1 \leq i \leq K)$ line contains integers $x_i, y_i$, separated by spaces.

Output (if no way of planting trees exists)

Output :( on $1$ line.

Output (if a way of planting trees exists)

Output $H+1$ lines as follows.

• On the $1$st line, output Yay!.
• For $1 \leq i \leq H$, on the $i+1$-th line, output a string of $W$ characters. The $j$-th ($1 \leq j \leq W$) character of the string must be as follows.
  • If square $(i, j)$ has a house: x
  • If square $(i, j)$ has no house and a tree is planted on that square: o
  • If square $(i, j)$ has no house and no tree is planted on that square: .

Constraints

• $1 \leq H, W \leq 2 \ 000$
• $0 \leq A_i \leq W$
• $0 \leq B_i \leq H$
• $1 \leq x_i \leq H$
• $1 \leq y_i \leq W$
• $0 \leq K \leq 16$
• $(x_i, y_i) \neq (x_j, y_j)$ $(i \neq j)$
• All inputs are integers.

Sample

3 3
1 1 1
1 1 1
3
1 1
2 2
3 3

Yay!
xo.
.xo
o.x

Yay!
x.o
ox.
.ox

4 5
3 2 3 2
1 3 2 2 3
3
1 2
2 3
4 4

:(

8 8
7 6 5 5 4 4 3 2
7 7 6 5 5 2 2 2
3
8 6
8 7
8 8

Yay!
ooooo.oo
oooooo..
ooooo...
ooooo...
ooo....o
oo...oo.
..ooo...
oo...xxx