**Time limit:**2.00 s**Memory limit:**512 MB

*Impatience*is a one-person game played on an infinitely large 2-dimensional grid. Each grid cell is either empty or it contains one pebble. We refer to grid cells with coordinates $(r,c)$, where $r$ is the row (numbered from top to bottom) and $c$ is the column (numbered from left to right).

You are given two shapes, A and B, that show the positions of the pebbles. In the beginning, you place all pebbles according to shape A, with the top left corner in cell $(1,1)$. Then you can perform a sequence of

**valid rotations**in which you move one pebble to a new position. You win if you find a sequence of rotations so that your final configuration looks like shape B (possibly shifted horizontally and vertically, but not rotated or mirrored).

A valid rotation is defined as follows. Let $r_1$ and $r_2$ be two adjacent rows (i.e., $|r_1-r_2| = 1$) and let $c_1$ and $c_2$ be two adjacent columns (i.e., $|c_1-c_2| = 1$). Now assume that:

- $(r_1,c_1)$ contains a pebble

- $(r_2,c_2)$ is empty

- exactly one of $(r_1,c_2)$ and $(r_2,c_1)$ contains a pebble.

Note that you are free to use both negative and positive coordinates. You can freely step outside the boundaries of the images A and B.

**Input**

As input, you will receive two shapes. Each shape is encoded as follows:

- One line with two numbers $n$ and $m$: the height and the width of the shape.

- $n$ lines, with $m$ characters on each line. The characters are either
`0`

or`1`

, indicating an empty slot or a slot with a pebble, respectively.

**Output**

If there is no way to win the game, output just

`-1`

.Otherwise, output a sequence of valid rotations that wins the game, encoded as follows. First, output one line which contains just one number $k$, the number of rotations. Then, output $k$ lines of the form "$r_1$ $c_1$ $r_2$ $c_2$", which indicates a rotation $(r_1,c_1) \to (r_2,c_2)$.

You can use at most 200000 rotations in your output.

**Limits**

- $1 \le n \le 15$

- $1 \le m \le 15$

- The number of pebbles in each shape is between 1 and 100.

**Example 1**

The following example corresponds to the above illustration.

Input:

`3 3`

001

111

100

2 4

1111

0010

Output:

`3`

1 3 2 4

2 2 3 3

3 1 2 2

**Example 2**

Input:

`2 5`

00000

11000

3 3

011

000

000

Output:

`0`

**Example 3**

Input:

`3 13`

0101010101110

0111010100100

0101010100100

1 1

1

Output:

`-1`

**Example 4**

Input:

`1 3`

111

3 2

01

01

10

Output:

`3`

1 3 0 2

1 2 0 3

0 3 -1 2