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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 9 1 3 5 8 2 2 5 1 0 0 0 0 0 0 0 4 2
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