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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 4 0 4 4 2 4 2 5 1 4 4 9 7 3 7 9 5 9 5 7 8 4 9 6 6
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