<|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:  3 4 8 8 8 6 4 6 3 4 0 0 0 0 0 6 8 7 1 2 1 3 4 5 6 5 4 7
Output: 8 8 8 6 4 6 3 4 0 0 0 0 0 6 8 7 1 2 1 3 4 5 6 5 4 7 3 4

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

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

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