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

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

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

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