<|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 3 1 5 1 5 1 4 8 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 3 1 5 1 5 1 4 8 1 1 0 0 0 0 0 0 0 0 0 0 0

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

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

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