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

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

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

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