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

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

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

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