You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
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In the land of Chaina, people pay each other in the form of links from chains. Fiona, originating from Chaina, has an open chain with  $2018$  links. In order to pay for things, she decides to break up the chain by choosing a number of links and cutting them out one by one, each time creating  $2$  or  $3$  new chains. For example, if she cuts the  $1111$ th link out of her chain first, then she will have  $3$  chains, of lengths  $1110$ ,  $1$ , and  $907$ . What is the least number of links she needs to remove in order to be able to pay for anything costing from  $1$  to  $2018$  links using some combination of her chains? 

*2018 CCA Math Bonanza Individual Round #10*
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In the land of Chaina, people pay each other in the form of links from chains. Fiona, originating from Chaina, has an open chain with  $2018$  links. In order to pay for things, she decides to break up the chain by choosing a number of links and cutting them out one by one, each time creating  $2$  or  $3$  new chains. For example, if she cuts the  $1111$ th link out of her chain first, then she will have  $3$  chains, of lengths  $1110$ ,  $1$ , and  $907$ . What is the least number of links she needs to remove in order to be able to pay for anything costing from  $1$  to  $2018$  links using some combination of her chains? 

*2018 CCA Math Bonanza Individual Round #10*
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