Problem Statement

A figure formed by joining squares of the same size edge to edge is called a polyomino. In the following, the side length of the squares that make up a polyomino is $1$.

Now, we define "type $C$ polyominoes" and "type $T$ polyominoes" as follows.

• Type $C$: a polyomino formed by joining $3$ or more squares in a straight line and then, from each of its two ends, joining $1$ or more squares in a straight line in the same direction
• Type $T$: a polyomino formed by joining, from $1$ square, $1$ or more squares in a straight line in each of exactly $3$ directions

• Polyominoes must not extend outside the grid, and different polyominoes must not overlap
• Each square that makes up a polyomino completely covers exactly $1$ cell of the grid

• Case $C$: only type $C$ polyominoes are used
• Case $T$: only type $T$ polyominoes are used
• Case $CT$: at least $1$ type $C$ polyomino and at least $1$ type $T$ polyomino are used

Constraints

• All input values are integers
• $2 \leq H, W \leq 200$

Input

The input is given from standard input in the following format.

$H\ W$

Output

Output the answer in the following format, where $output_C, output_T, output_{CT}$ denote the outputs for case $C$, case $T$, and case $CT$, respectively.

$output_C$
$output_T$
$output_{CT}$

For each case, if no tiling satisfying the conditions exists, output -1; if one exists, output one example in the following format.

$K$
$A_{1, 1}\ A_{1, 2}\ \cdots\ A_{1, W}$
$A_{2, 1}\ A_{2, 2}\ \cdots\ A_{2, W}$
$\vdots$
$A_{H, 1}\ A_{H, 2}\ \cdots\ A_{H, W}$

$K$ is the number of polyominoes used, and $A_{i, j}$ is an integer between $1$ and $K$, inclusive, representing the polyomino that covers the cell in the $i$-th row from the top and the $j$-th column from the left of the grid.
Denoting the cell in the $i$-th row from the top and the $j$-th column from the left by $(i,\ j)$, it must hold that $A_{i_1, j_1} \neq A_{i_2, j_2}$ when the polyominoes covering $(i_1,\ j_1)$ and $(i_2,\ j_2)$ are different, and $A_{i_1, j_1} = A_{i_2, j_2}$ when they are the same.

Print a newline at the end.

See also the samples below for the details of each case and the output format.

Sample

Sample 1

Input

4 5

Output

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

The figure below illustrates the sample output.
In this example, the tiling uses $3$ type $C$ polyominoes in case $C$,
$4$ type $T$ polyominoes in case $T$,
and a total of $3$ polyominoes, namely $1$ type $C$ polyomino and $2$ type $T$ polyominoes, in case $CT$.

2 2

-1
-1
-1