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

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

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

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