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

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

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

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 0 0 3 8 3 2 3 5 6 5 6 1 8 9 7 2 7 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