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

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

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

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