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 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 5 4 4
Output: 5 4 4 4 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8

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

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

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