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

Example 2:
Input:  9 4 3 4 4 3 4 2 0 0 0 0 0 0 0 0 0 0 0 7 7 2 7 7 5
Output: 2 7 7 5 9 4 3 4 4 3 4 2 0 0 0 0 0 0 0 0 0 0 0 7 7

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

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