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

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

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

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