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:  3 7 2 0 0 0 0 0 0 0 0 0 2 3 2 2 8 9 1 8 5
Output: 1 8 5 3 7 2 0 0 0 0 0 0 0 0 0 2 3 2 2 8 9

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

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

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