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

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

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

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