What alghorithm can I use to find the biggest subarray within a 2d array with only n different numbers?

Let's say I have a 2d array 100x100 in size, each cell in that array has a number from 1 to 50 randomly.

How do I find the biggest subarray in a rectangle size in that array that has only n different numbers?

Small example:

array: 1 2 3 3 3 2 2
       7 4 3 3 4 9 8
       1 2 3 3 3 4 2
       7 6 1 9 9 4 2
In this case the biggest sub rectangle with only 1 number allowed would be 
       3 3
       3 3
With 2 numbers allowed it would be
       3 3 3
       3 3 4
       3 3 3

Does something for this exist?