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

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

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

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