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

Example 2:
Input:  4 1 2 4 7 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3
Output: 0 0 4 3 4 1 2 4 7 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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