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

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

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

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