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

Example 2:
Input:  9 6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 4 2
Output: 2 4 2 9 6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 5 6 7 5 1 4 4 6 2 3 1 1 8 6 7 5 3 0 0 0 0 0 0 0 0 0 0 0 7
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