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

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

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

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