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

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

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

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