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Elf Chalkboard Puzzle

I write the integers 1-9999 (inclusive) on a huge chalkboard. Each number is written once.
During the night the board is visited by a series of naughty math elves (it’s a thing!)
Each elf approaches the board, selects two numbers at random, erases them, and replaces them with a new number that is the absolute difference of the two numbers erased.
This vandalism continues all night until there is just one number remaining.
I return to the board the next morning and find the single number of the board. The question is: Is this remaining number odd or even?
Is this remaining number odd or even?