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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 9 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 9

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

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

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