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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 5 5 4 8 9 9 4 1 1 7 8 2 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 1 6 5 5 4 8 9 9 4 1 1 7 8 2 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 1 6 7 6 3 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 8 6 4 1 2 8 7
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