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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 2 3 5 8 8 8 3 9 0 0 9 2 7 6 2 6 7 3 4 2 9 1 5 5 2
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