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

Example 2:
Input:  3 3 8 3 2 7 1 2 4 0 0 0 0 0 0 0 0 0 0 0 0
Output: 8 3 2 7 1 2 4 0 0 0 0 0 0 0 0 0 0 0 0 3 3

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

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