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:  5 9 6 4 3 1 4 8 1 2 4 5 4 1 1 6 6 6 8 4 1 1 2 4 6 1 9
Output: 3 1 4 8 1 2 4 5 4 1 1 6 6 6 8 4 1 1 2 4 6 1 9 5 9 6 4

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

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

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