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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 5 0 0 0 0 0 0 0 0 0 0 0 2 6 6 9 6 7 8 8 5 3 9 2 7 4 5 4 8
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