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:  6 3 9 7 5 3 0 0 0 0 0 6 8 7 9
Output: 5 3 0 0 0 0 0 6 8 7 9 6 3 9 7

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

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

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