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

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

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

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