# A Complex Function

The first $$50$$ natural numbers are written on a board. You apply the following operation $$49$$ times, until you arrive at one final number:

• Select any two numbers from the board, $$a$$ and $$b$$.

• Erase those two numbers, and replace them with $$|a-b|$$.

Determine the sum of all possible values for the final value remaining number on the board.

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