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

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

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

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