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

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

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

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