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 5 5 0 0 0 0 0 0 0 0 0 0 0 9 3
Output: 0 0 0 0 0 0 0 0 0 0 0 9 3 7 5 5

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 6 3 1 4 9 6 4 9 8 7 0 0 0 0 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