Problem

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The number $1234$ is written on the board. A play consists of subtracting a non-zero digit of that number from that number, and replacing the number by the result. The player who writes the number (not digit) zero wins. Determine if there is a winning strategy for one of the two players who play consecutively. Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it )