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

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

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

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