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

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

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

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