What is the smallest positive integer $n$ for which $(12{,}500{,}000)\cdot n$ leaves a remainder of $111$ when divided by $999{,}999{,}999$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the smallest positive integer $n$ for which $(12{,}500{,}000)\cdot n$ leaves a remainder of $111$ when divided by $999{,}999{,}999$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8{,}880
What is the smallest positive integer $n$ for which $(12{,}500{,}000)\cdot n$ leaves a remainder of $111$ when divided by $999{,}999{,}999$?
train