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

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

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

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