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

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

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

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