<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 0 0 4 9 9 4 8 6 7 5 9 9 3 6 1 3 0 0 0 0 0 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user