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

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

Example 3:
Input:  5 6 3 3 0 0 0 0 0 0 0 0 0 0 0 0 8
Output: 6 3 3 0 0 0 0 0 0 0 0 0 0 0 0 8 5

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 3 0 0 0 0 0 4 5 6 4 3 1 3 3 3 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