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 6 0 0 0 6 6 3 8 0 4 5 0 4 7 4 2 8 0 2 1 2 0 2
Output: 0 0 0 0 0 0 0 0 6 6 6 3 8 4 5 4 7 4 2 8 2 1 2 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 5 7 0 6 5 0 8 3 9 5 2 0 0 0 8 0 0 1 0 0 1 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