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 4 8 5 5 1 1 1 9 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9
Output: 5 5 1 1 1 9 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 8 8 4 8

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

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

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