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

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

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