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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 1 6 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 1 6 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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