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

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

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

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