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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 1 1 9 2 5 3 2 9 2 3 3 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 1 1 9 2 5 3 2 9 2 3 3 0 0 0 0 0 0 0 0 0 0 0 0

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

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