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

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

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

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