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

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

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