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

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

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

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