<|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:  4 3 7 6 8 6 6 6 2 2 8 3 7 3 5 4 0 5 9 6 7 6 7 3 4 9 4 6 8
Output: 8 4 3 7 6 8 6 6 6 2 2 8 3 7 3 5 4 0 5 9 6 7 6 7 3 4 9 4 6

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

Example 3:
Input:  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 6 4 6
Output: 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 6 4

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