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:  4 1 6 8 9 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 9 8 7 1 6 7 4 6 4 1
Output: 8 9 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 9 8 7 1 6 7 4 6 4 1 4 1 6

Example 2:
Input:  1 5 4 2 4 1 3 1 5 2 6 6 2 5 2 9 8 1 7 2 0 0 0 0 0 0 0 0 7 4
Output: 2 4 1 3 1 5 2 6 6 2 5 2 9 8 1 7 2 0 0 0 0 0 0 0 0 7 4 1 5 4

Example 3:
Input:  8 5 0 0 8 8 7 4 7 2 3 2 5 9 5 4 2 7 6 5 5 3 3 5 6 7 6 5 2 2
Output: 0 8 8 7 4 7 2 3 2 5 9 5 4 2 7 6 5 5 3 3 5 6 7 6 5 2 2 8 5 0

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