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

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

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

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