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

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

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

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