<|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
 The digits from 1 to 9 are written in order so that the digit \( n \) is written \( n \) times. This forms the block of digits \( 1223334444 \cdots 999999999 \). The block is written 100 times. What is the \( 1953^{\text{rd}} \) digit written? Express your answer as a single digit. 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
6
The digits from 1 to 9 are written in order so that the digit \( n \) is written \( n \) times. This forms the block of digits \( 1223334444 \cdots 999999999 \). The block is written 100 times. What is the \( 1953^{\text{rd}} \) digit written? Express your answer as a single digit.
test