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

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

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

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