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1386. Maze

Time limit: 0.5 second
Memory limit: 64 MB
One of the most popular games of all times is the "Maze". The game is played on a N × M table. The player can make the instructions: 'left', 'right', 'up', 'down'. For each cell of the table and each instruction the game-master has defined the destination cell that the player moves to; that is, the player is given the map of the maze. Once a game was interrupted, and the master has forgotten which cell the player was in. Fortunately, a full record of the gameplay has remained, which is the sequence of the instructions made by the player. You are to write a program determining the cells that the player can be currently in.

Input

The first line of the input contains two numbers N and M (1 ≤ N,M ≤ 100). Four blocks of N lines each follow. Each line contains M pairs, being the new coordinates of the player after making k'th instruction standing in the cell (j, i), where i is the number of pair in the line, j is the number of line in the block, and k is the number of block. Following is the number S (1 ≤ S ≤ 4000) of the instructions made by the player. The last line contains the S numbers of the instructions made.

Output

The first line of the output must contain the number L of the cells that player can be in after making the given sequence of instructions. Each of the next L lines must contain the coordinates of these cells, ordered first by the first coordinate, and then by the second.

Sample

inputoutput
```2 3
1 2  1 3  1 3
2 2  2 3  2 3
2 1  2 2  2 3
2 1  2 2  2 3
1 1  1 1  1 2
2 1  2 1  2 2
1 1  1 2  1 3
1 1  1 2  1 3
4
1 2 3 4```
```2
1 1
1 2```
Problem Author: Andrew Khalyavin
Problem Source: Petrozavodsk summer training camp, August 2005.
Tags: none