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

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

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

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