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

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

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

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