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Number Theory Level pending

Let \(r\) be the remainder of:

\[1+2^2+3^3+4^4+5^5+6^6+7^7+8^8+9^9+10^{10}\]

when divided by \(3\), and \(s\) the sum of the last digits of each of the terms of the sum above. What is \(r+s\)?

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