A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  0 4 2 6 4 4 1 5 8 1 8 9 6 3 2 5 4 9 0 0
Output: 0 0 0 4 2 6 4 4 1 5 8 1 8 9 6 3 2 5 4 9

Example 2:
Input:  4 6 6 9 5 3 9 4 1 3 3 6 4 9 3 8 7 7 1 1
Output: 1 1 4 6 6 9 5 3 9 4 1 3 3 6 4 9 3 8 7 7

Example 3:
Input:  6 2 0 0 0 0 0 0 0 0 0 0 6 9 7 9 9 3 5 8
Output: 5 8 6 2 0 0 0 0 0 0 0 0 0 0 6 9 7 9 9 3

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 2 9 6 1 1 5 1 9 3 4 2 1 7 8 4 6 0 0 1
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user