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

Example 2:
Input:  7 6 3 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 4
Output: 0 0 0 4 7 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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