<|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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0

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

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

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