Let the remainder when \( 2^{7,812,530}\) is divided by \(10,000,000,000\) be \(N\). Find the digit sum of \(N\).

\(Notes\) \(and\) \(Assumptions:\) The digit sum of a number is the sum of the number's digits. For instance, \(2014\) has a digit sum of \(7\) because \(2+0+1+4=7\)

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