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

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

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

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