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

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

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

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