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

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

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

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