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

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

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

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