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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 7 9 4 2 8 2 2 0
Output: 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 7 9 4 2 8

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

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