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

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

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

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