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

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

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

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