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

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

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

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