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:  9 9 2 3 4 4 4 6 9 5 4 6 6 1 4 9 7 8
Output: 9 7 8 9 9 2 3 4 4 4 6 9 5 4 6 6 1 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 5 1 4 2 4 1 1 8 3 9 4 6 7 1 2 1 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