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

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

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

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