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:  8 7 7 4 3 5 0 0 0 0 0 0 0 0 0 7 4 4 6 9 6 1 4
Output: 9 6 1 4 8 7 7 4 3 5 0 0 0 0 0 0 0 0 0 7 4 4 6

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

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