<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 For any real number sequence $A=\left\{ {{a}_{1}},{{a}_{2}},{{a}_{3}},\cdots \right\}$, define $\Delta A$ as the sequence $\left\{ {{a}_{2}}-{{a}_{1}},{{a}_{3}}-{{a}_{2}},{{a}_{4}}-a{}_{3}^{{}},\cdots \right\}$, whose $n$th term is $\left({{a}_{n+1}}-{{a}_{n}}\right)$. Suppose that all terms in the sequence $\Delta \left( \Delta A \right)$ are $1$, and ${{a}_{18}}={{a}_{2017}}=0$, then ${{a}_{2018}}=$_______ Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1000
For any real number sequence $A=\left\{ {{a}_{1}},{{a}_{2}},{{a}_{3}},\cdots \right\}$, define $\Delta A$ as the sequence $\left\{ {{a}_{2}}-{{a}_{1}},{{a}_{3}}-{{a}_{2}},{{a}_{4}}-a{}_{3}^{{}},\cdots \right\}$, whose $n$th term is $\left({{a}_{n+1}}-{{a}_{n}}\right)$. Suppose that all terms in the sequence $\Delta \left( \Delta A \right)$ are $1$, and ${{a}_{18}}={{a}_{2017}}=0$, then ${{a}_{2018}}=$_______
test