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

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

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

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