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:  0 0 4 9 4 2 3 3 3 1 2 1 2 8 9 3 1 6 7 8 9 2 1
Output: 8 9 2 1 0 0 4 9 4 2 3 3 3 1 2 1 2 8 9 3 1 6 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 7 0 0 0 0 0 0 0 0 0 3 3 2 5 2 3 5 6 8 3 3 1
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