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 9 5 8 1 4 4 7 7 4 8 4 3 6 3 9 6 6 0 0
Output: 6 6 0 0 1 9 5 8 1 4 4 7 7 4 8 4 3 6 3 9

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 1 9 5 0 0
Output: 9 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 1

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 3 7 3 0 0 0 0 0 4 1 7 7 3 9 2 3 8 9 6
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