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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 6 7 4 1 1 5 0 0 0 0 1 5 8 7 6 1 2 9 7
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