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

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

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

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