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

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

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