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:  3 5 7 5 2 6 6 1 7 4 2 7 6 1 2 1 6 5 4 1 4 5 2 7 4 7 2 1 1 6
Output: 6 1 1 2 7 4 7 2 5 4 1 4 5 6 1 2 1 6 7 2 4 7 1 6 6 2 5 7 5 3

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

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

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