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

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

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

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