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

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

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

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