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

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

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

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