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

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

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

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