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 9 9 8 2 5 2 9 2 3 1 4 2 8 2 8 9 5 5
Output: 8 2 5 2 9 2 3 1 4 2 8 2 8 9 5 5 2 9 9

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

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

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