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

Example 2:
Input:  4 0 9 0 0 0 0 0 0 0 0 6 0 0 6 0 0 0 4 0 0 0 0 0 0 0 9 6 7
Output: 4 9 6 6 4 9 6 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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