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

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

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

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