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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 4 9 4 3 8 8 8 5 2 7 6 5 6 4 8 1 5 5 4 7 4 2 0 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