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:  8 8 6 8 8 8 8 4 8 7 8 8 9 8 8 8 8 8 8 4 8 8 8 8 3 8
Output: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

Example 2:
Input:  6 6 6 6 6 6 6 6 6 6 3 6 6 6 6 5 6 6 6 6 8 6 6 9 6 6
Output: 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

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

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