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:  4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 5 1
Output: 0 9 5 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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

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