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

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

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

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