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C. Dungeons and Candies

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDuring the loading of the game "Dungeons and Candies" you are required to get descriptions of *k* levels from the server. Each description is a map of an *n* × *m* checkered rectangular field. Some cells of the field contain candies (each cell has at most one candy). An empty cell is denoted as "." on the map, but if a cell has a candy, it is denoted as a letter of the English alphabet. A level may contain identical candies, in this case the letters in the corresponding cells of the map will be the same.

When you transmit information via a network, you want to minimize traffic — the total size of the transferred data. The levels can be transmitted in any order. There are two ways to transmit the current level *A*:

- You can transmit the whole level
*A*. Then you need to transmit*n*·*m*bytes via the network. - You can transmit the difference between level
*A*and some previously transmitted level*B*(if it exists); this operation requires to transmit*d*_{A, B}·*w*bytes, where*d*_{A, B}is the number of cells of the field that are different for*A*and*B*, and*w*is a constant. Note, that you should compare only the corresponding cells of levels*A*and*B*to calculate*d*_{A, B}. You cannot transform the maps of levels, i.e. rotate or shift them relatively to each other.

Your task is to find a way to transfer all the *k* levels and minimize the traffic.

Input

The first line contains four integers *n*, *m*, *k*, *w* (1 ≤ *n*, *m* ≤ 10; 1 ≤ *k*, *w* ≤ 1000). Then follows the description of *k* levels. Each level is described by *n* lines, each line contains *m* characters. Each character is either a letter of the English alphabet or a dot ("."). Please note that the case of the letters matters.

Output

In the first line print the required minimum number of transferred bytes.

Then print *k* pairs of integers *x*_{1}, *y*_{1}, *x*_{2}, *y*_{2}, ..., *x*_{k}, *y*_{k}, describing the way to transfer levels. Pair *x*_{i}, *y*_{i} means that level *x*_{i} needs to be transferred by way *y*_{i}. If *y*_{i} equals 0, that means that the level must be transferred using the first way, otherwise *y*_{i} must be equal to the number of a previously transferred level. It means that you will transfer the difference between levels *y*_{i} and *x*_{i} to transfer level *x*_{i}. Print the pairs in the order of transferring levels. The levels are numbered 1 through *k* in the order they follow in the input.

If there are multiple optimal solutions, you can print any of them.

Examples

Input

2 3 3 2

A.A

...

A.a

..C

X.Y

...

Output

14

1 0

2 1

3 1

Input

1 1 4 1

A

.

B

.

Output

3

1 0

2 0

4 2

3 0

Input

1 3 5 2

ABA

BBB

BBA

BAB

ABB

Output

11

1 0

3 1

2 3

4 2

5 1

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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