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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 2 5 1 5 1 4 8 9 1 8 0 4 8 3 5 2 8 3 3 2 8 6 1 6 9 3 8 5 4
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