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

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

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

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