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:  8 9 2 6 0 0 0 0 0 0 0 4 1 8 2 4 1 9 9 2 8 4 5 3
Output: 5 3 8 9 2 6 0 0 0 0 0 0 0 4 1 8 2 4 1 9 9 2 8 4

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

Example 3:
Input:  0 0 0 0 0 0 0 7 5 6 9 3 7 6 7 8 9 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 7 5 6 9 3 7 6 7 8 9 0 0 0 0 0

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