<|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:  5 6 3 2 8 1 8 0 8 2 7 2 6 1 8 6 2 7 8 1 5 6 3 1 4 7 1 6 5
Output: 6 3 2 8 1 8 0 8 2 7 2 6 1 8 6 2 7 8 1 5 6 3 1 4 7 1 6 5 5

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

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

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