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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 5 3 8 8 4 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 5 3 8 8 4

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