<|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:  4 3 2 0 3 6 3 6 3 8 2 3 4 1 1 9 2 7 5 5 7 7 6 6 3 9 8
Output: 0 3 6 3 6 3 8 2 3 4 1 1 9 2 7 5 5 7 7 6 6 3 9 8 4 3 2

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

Example 3:
Input:  3 7 7 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 7 7

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