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

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

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

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