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

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

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

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