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:  2 4 6 0 0 0 0 0 0 0 0 0 0 0 6 2 7 5 4 9 5 6 2 5 6 9 3 3
Output: 9 3 3 2 4 6 0 0 0 0 0 0 0 0 0 0 0 6 2 7 5 4 9 5 6 2 5 6

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 1 8 7 6 7 3 8 1 3 6 8 5 2 0 0 0 0 0 0 0 0 0 0 0 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