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

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

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

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