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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 1 4 8 7 6 2 7 2 1 3 9 8 6 9 9 5 7 7 7 8 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