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

Example 2:
Input:  7 5 1 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 5 5 1 8 1 3 1 3
Output: 3 1 3 7 5 1 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 5 5 1 8 1

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