Find the smallest integer \(n\) such that \( 2^n \) starts with **10 nines**.

\[2^n = \underbrace{\overline{9999999999......abcdefghij}}_{\text{A few hundred million digits}}\]

What is the **sum** of last 10 digits of the smallest number **\(2^n\)**, namely \(a+b+c+d+e+f+g+h+i+j =? \)

**Note**: There are infinitely many **n** such that \(2^n\) starts with 10 nines. We are looking for the smallest such **n**.

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