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

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

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

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