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

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

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

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