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

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

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

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