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

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

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

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