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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 8 5 2 7 2 6 8 2 4 9 3 1 4 1 5 8 0 0 0 0 0 0 5 2 3
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