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

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

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

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