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

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

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

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