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:  4 8 7 9 0 0 0 0 9 1 5 2 8 7 2 7 8
Output: 9 0 0 0 0 9 1 5 2 8 7 2 7 8 4 8 7

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

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

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