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

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

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

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