# Good Arrays

Consider a $$7 \times 7$$ array, each of whose cells is filled up by an integer between $$1$$ and $$49$$ (inclusive). Every cell has exactly one number written on it, and every number between $$1$$ and $$49$$ appears exactly once.

An operation on the array is defined as follows:

• Select a row / column of the array.
• Either add $$1$$ to all numbers in that row / column or subtract $$1$$ from all numbers in that row / column.

An array is said to be good if there exists a finite sequence of operations after which all cells have the same number written on them. Find the last three digits of the number of good arrays.

Details and assumptions

• A row / column can be operated on as many times as wanted.
• You might use the fact that $$7$$ is a prime.
• This problem is not original.
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