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:  7 7 6 7 1 8 1 0 0 0 0 0 0 8 3 6 3
Output: 3 7 7 6 7 1 8 1 0 0 0 0 0 0 8 3 6

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 1 9 2 3 8 1 4 4 1 9 9 0 4 6 6 6
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