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:  2 2 1 5 5 1 7 2 9 1 7 2 0 6 2 6 8 3 7 9 3
Output: 3 2 2 1 5 5 1 7 2 9 1 7 2 0 6 2 6 8 3 7 9

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

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

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