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

Example 2:
Input:  5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5

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

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