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:  1 8 5 5 5 3 0 0 0 0 0 0 0 0 0 0 0 0 1 7 1 2 4 6 2 4 8 4
Output: 2 4 8 4 1 8 5 5 5 3 0 0 0 0 0 0 0 0 0 0 0 0 1 7 1 2 4 6

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

Example 3:
Input:  4 7 4 5 9 8 9 5 2 1 5 8 5 4 0 0 0 0 0 0 0 0 0 0 0 0 4 4
Output: 0 0 4 4 4 7 4 5 9 8 9 5 2 1 5 8 5 4 0 0 0 0 0 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 6 3 8 6 9 7 4 1 9 8 3 1 5 7 2 1 7 6 4 2 5 3 0 0 7 6 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