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

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

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

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