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 8 3 5 5 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1 3 1 2
Output: 3 1 2 7 8 3 5 5 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1

Example 2:
Input:  1 5 0 0 0 0 0 0 0 0 0 0 6 8 4 5 6 1 1 9 1 2 6 7 3 6 5 8 3
Output: 5 8 3 1 5 0 0 0 0 0 0 0 0 0 0 6 8 4 5 6 1 1 9 1 2 6 7 3 6

Example 3:
Input:  5 7 9 3 5 1 2 6 5 1 1 7 4 9 8 0 0 0 0 0 0 0 0 2 8 4 9 1 8
Output: 9 1 8 5 7 9 3 5 1 2 6 5 1 1 7 4 9 8 0 0 0 0 0 0 0 0 2 8 4

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 4 5 7 6 8 7 6 3 6 3 0 0 0
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