# Interesting transition.

Level pending

A positive integer $$x$$ has $$3$$ distinct prime factors, $$a$$, $$b$$, and $$c$$, so that $$abc=x$$. Another positive integer, $$y$$, which equals to $$x+1$$, has $$3$$ distinct prime factors, $$a-1$$, $$b+7$$, $$c-8$$.

What are the last three digits of the sum $$a+b+c+x+y$$?

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