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:  6 9 6 2 2 2 2 5 8 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 2 2 2 5 8 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 9 6 2

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

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

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