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

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

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

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