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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 0 0 0 0 3 6 8 2 3 5 8 4 8 9 8 6 5 7 2 7 5 5 1 9 2 2 2 7
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