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

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

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

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