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

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

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