<|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:  1 3 1 6 4 6 1 7 7 0 0 0 0 0 0 0 6 6 4 9 1 4 3 3 9 6 7 4
Output: 6 4 6 1 7 7 0 0 0 0 0 0 0 6 6 4 9 1 4 3 3 9 6 7 4 1 3 1

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

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

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