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

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

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

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