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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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