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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 1 0 4 0 0 0 0 7 7 4 7 8 6 0 4 0 9 2 7 1 7 7 0 2 2 0
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