Since getting his job at Iceberg Corporation, Rami has been ignoring his tasks and playing a new game called Grid Crash. It is a game played on a grid $$$G$$$ of size $$$n\times m.$$$ Each cell in the grid either has some colour, or is empty.

Initially, each cell $$$(i,j)$$$ in the grid contains some color $$$c_{i,j}.$$$ The grid itself contains at most 4 distinct colours.

Now the game is played as follows:

• Rami selects some cell $$$(i,j)$$$ with color $$$c_{i,j}$$$ and removes the color.
• This induces a chain reaction, on which adjacent cells of $$$(i,j)$$$ with the same color are also removed. Also, the adjacent cells of those that have color $$$c_{i,j}$$$ are removed, and so on.
• After that, each non empty cell $$$(a-1,b)$$$ that is on top of an empty cell $$$(a,b)$$$ will swap their content. That is, $$$(a-1,b)$$$ will be empty, and $$$(a,b)$$$ will contain $$$c_{a-1,b}.$$$ This will be repeated until all empty cells will be on top of colorful cells.
• After that, if we have a column $$$C_{i}$$$ of empty cells, then we swap its content with $$$C_{i+1}.$$$ This will be repeated until empty columns will be at the rightmost.
• Rami will repeat step 1 until the grid has no remaining color.

Now, Rami wants to finish the game in the fewest moves possible. Please help him.