One two three four .... where do they stop

Algebra Level 3

The total number of digits in 1 0 10 0 100 0 10000 10^{100^{1000^{10000}}} can be expressed as A + 1 0 B 1 0 C A + 10^{B*10^{C}} then A + B + C is?

20002 40004 30003 10001

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