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

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

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