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

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

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

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