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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 2 1 5 4 1 6 6 4 9 2 6 4 5 3 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